Did you miss the part where they explained that Angel was given his human soul back, ergo he was essentially the very human Liam forced to deal with 145 years of horrific, new memories of a demon stuffed in his head. Angel with a soul is both a human and a demon. A dead human man whose corpse was hijacked by a demonic parasite having his human self stuffed back in, then forced to deal with demonic urges and survival needs.
The being who fell in love with Buffy was very much a human man and that was actually part of the problem. Angel said it himself. "It's not the demon in me that needs killing, Buffy. It's the man."
Liam/Angel was arguably as new to love as Buffy was. Liam and Angelus may have been debauched, but those feelings of shared empathy over their loneliness at being the only ones of their kinds straddling two words, yet accepted by neither, and understanding true, selfless, sacrificial love were quite new. But it was ultimately the temptations of the human Liam/Angel who were the biggest threat, as it was his human, not demonic, temptation that triggered Angelus. And yet, at every stage, he was always the one trying to pull back from the relationship (right up through the end of Surprise) until Buffy and Willow guilt-tripped him for staying away. Rather importantly, he was completely innocent to the rules of his ensoulment. Until Angel had to put the halt on the relationship for the world's sake, and despite his many warnings that he spoke aloud all along right from the beginning (what he says in 1x07 and Bad Eggs is practically the breakup speech verbatim), he very much let Buffy be in control of every step in their relationship moving forward. He was the one usually trying to slow it down and urge against it at every step.
Nobody was sweeter to Buffy when it came to listening to her talk about her days, urging her to think about the future (ultimately revealing his own greatest desire: fatherhood--for all the talk of him not being an open book about himself, this was a huge reveal that had profound impact on his own arc), trying to find ways to connect her to her human life before being the Slayer and sharing words of wisdom on everything from parental issues to self-worth if not for powers to why they fight.
He was indeed a "perfect gentleman" when it came to the human aspects of courtship, despite being what he is. He was vicariously also living the part of a human man in love that he very much desired to be. It's yet another reason he's so reluctant for her to witness his demonic side, despite her best efforts to quell his unease. We see this not only with her touching and kissing his game face, but him being visibly uncomfortable with his dietary habits being witnessed--even when she was the one bringing him blood from the butcher. And of course, his initial refusals to save his own life by feeding on her until she forced him. Despite her efforts at demonstrating her comfortableness around his inhumanity, he very much wanted her to see him as human. Angel ultimately did get a bit more comfortable around his team later, but even then you often saw his desire for them to see him as just a man instead of a monster. He reveled in human activities such as fixing scrambled eggs for the humans he was caring for. That was always Angel. He's the monster who desperately wants to be human, even if he also wants it to be earned.
Liam had always been capable of love, as we saw with his sister Kathy, but it was overwhelmed by what actually seems to have been bitterness born out of having interests that could never be realized (Liam hints at it with his line, "I always wanted to see the world, but...") and his inability to be what his father wanted him to be (likely a linen and silk merchant) rather than what *he* wanted to be. What do we see as common traits in both Angelus and Angel? Both human and demon are extremely intelligent artists, art collectors, lovers of the arts and world travelers who speak numerous languages. Seems that's what Liam felt denied before he drowned himself in bitterness, booze and wenches. We hear hints from Angel that Liam was also driven to looking for something other than what his own time could provide as far as exciting women went, so went looking in all the wrong places until it literally killed him. There's a lot more continuity (on a deeper level, not just the surface) between Liam and Angel than many pretend.
It's incorrect to say that a vampire with a soul isn't also capable of being a human *and* a boyfriend. The soul means that a being that was born very much human is literally in control of their old body, even if it's no longer a human body. And thus, when it comes to being a boyfriend, it's very much that remaining, still-surviving human side being emotionally nourished after a long drought.
Nobody tried harder to keep Buffy connected to her human life and to life outside of being the Slayer as a means to give her something to live for. He was the one who always tried to urge her to consider what she might want in a future that he could never give her, but wanted nothing more than for her to have everything he never could. Angel was always the big picture thinker thinking of the best possible future, even if it was the decision that hurt the most in the short term. He sacrificed his own happiness most of all.
But he also had a self-identity much stronger than merely being a boyfriend, as like Buffy, he understood that their lives were not their own. Yet, at the same time, he also knew that both of them needed something to live for and to tie them to the world they were trying to help. Angel was the most equal of all of Buffy's boyfriends, as he's the only one who knows what it's like to be as much of a lonely, unique Atlas-esque hero straddling two worlds they don't fit in as she is. Riley and Spike are far more comfortable as followers of organizations or teams than they are as the leaders making the hard, often horrible decisions like Buffy and Angel. However, Angel is more apt to make the harder choices himself, even if Wesley certainly learned from the master. While Buffy certainly had to make her share of terrible choices (more of them in the early seasons, I'd argue!--Prophecy Girl and Becoming showcase Buffy at her most selfless, sacrificial best making the hardest decisions of her life), unwillingness to kill evil humans became a major problem to the point where Giles had to step in. Angel, of course, spends most of his show dealing with a significant amount of very human evils.
As far as the relationship decision went, it's quite important that Buffy acknowledged that even though she desperately didn't want to face it, she knew everything Angel said to her during their breakup was right. On the contrary, Giles was particularly concerned that Spike didn't have the self-awareness and insight to leave as Angel had done.
As far as Riley goes, it wasn't just the final nails in the coffin in season 5. It's really The Yoko Factor where the end of Briley is spelled out. It wasn't even just merely meeting the ex and coming up short. Note that Riley very much began that fight that Angel spent the whole time just trying to get away from (kept trying to go for the ladder to the roof) while being jumped and attacked with no benefit of the doubt. Not only did Riley accuse Angel of being Angelus, but also accused Buffy of being unfaithful and turning Angel into Angelus, despite all evidence to the contrary displayed by the fact that Angel really just wanted to get away from the soldiers that jumped him and didn't kill any of them. Riley also rubbed in one of Angel's greatest insecurities (as Spike did again in Destiny), which is how he lost his soul and the nature of his curse, but that's not remotely the worst of what Riley says. Riley crossed the line when he accused his girlfriend of being unfaithful to him and straight up insinuated that she slept with her ex. Boy, did Riley not trust Buffy. Not that Xander's words helped (behold the source) in both this case and when he tried to guilt Buffy into thinking Riley was the one even after he had cheated on her and guilt-tripped her over caring more about her dying, hospitalized mother than him. The red flag behavior is right there in season 4.