I understand these things happen, and things in the heat of the moment are said (of course it could all be premeditated as well, depending on who you're dealing with), but no amount of understanding from anyone will change anything that you may have said (for example: "Never come see me, or speak to me again"), and no amount of understanding from anyone will change the life that you chose to lead.
Of course, if you only notice that someone matters, only when you see them to start going out of your reach, and see them moving on because you didn't bother to treat them as they mattered, then my friend, that is not love. That is more like obsession.

A lifetime later and I still feel the same way

A countdown clock starts after that. You can't read the numbers, you just know they're changing...
If nobody tries to retrieve the situation, the damage festers and eventually kills the relationship. And then it's all gone.
Everybody loses. You get to wonder what could have been. Maybe for the rest of your life.
Don't be that person. If you try to fix it and fail, at least you'll know you did whatever you could think of, to make it work again. I tried and failed. Life is like that sometimes.
I miss her horribly, still. But it just is.

Regardless of what’s said by either person in a heated moment, if both people don’t want it enough to fight for it then the relationship is going to die. Some relationships are complicated and full of passion and disagreements and others are quiet and uncomplicated and maybe a little passionless. I’d choose passion any day because I’m not afraid of a disagreement as long as my partner has the maturity to have an actual conversation about things and doesn’t just refuse to be accountable or refuse to compromise or whatever else makes having a relationship with them impossible. People who truly do love someone don’t just meekly give up when the other person gets upset and tries to communicate why they are and tries to get them to work on it. People who truly do love the other person also don’t start dating other people immediately. That’s not love at all in my opinion because someone who has a broken heart isn’t just going to snap out of it that fast. I see people doing that (usually guys) and they’re the same ones who don’t really care about the other person’s feelings at all, including the new person who is usually just being used for sex and so they don’t have to be alone. Then there’s the people who always have someone waiting in the wings that usually they’re keeping in touch with while they’re still with their supposed partner. So I agree with the Op that real love is something you fight for if you have the guts to get over your pride.

@ifitmatters
That's a nice theory.
Breaks down when the other person tells you that you're a bad fit and they're done with you. A very final thing to hear, and there's nothing to fight for. Because "fighting" is stalking after that point.
So, no, no purpose to hanging around and harassing the other person. If one party says something that final, they have to explicitly take it back, and soon, or there's nothing more to be done.
Generalizing is not helpful. It always, ALWAYS comes down to the particular circumstances, and options for men specifically are very limited. "Fighting" not permitted, and maybe even legally actionable. If a guy tries to reach out a week later and patch things up, and is told that it's just not a good fit and there's nothing to be done, there's nowhere to go from there.
If a guy find someone else (or is found by them) after being cut off like that, there's no reason to linger and wait for the other party to MAYBE think differently. If they cut you off once and didn't rethink it quickly, they'll do so again. People change slowly when they change at all, and they hardly ever learn to not just drop somebody like that.
If they treated you so casually, badly and with such finality once, they will do so again. Especially if they know you'll keep trying to fix it.
What is rewarded, will be repeated. Bad behavior even more so.

I did say “both people”. Obviously if one person isn’t willing to fight for it then there’s no hope for it. The point is though, that if you have a huge disagreement with someone you love, but then when emotions calm down a bit you regret it, and if you choose to simply do nothing to try to fix the situation then in my books that means that it didn’t matter enough.

Of course there’s always another point of view, particularly if you’re the person who was actually IN the relationship, not just someone speaking for them, in which case you’re not qualified to make an informed point of view. For example, if the person that did the breaking up did so for a very good reason and also gave the other person lots of opportunities to try to fix it. If the person who was left chose to make no effort to change or to even acknowledge that anything the person said had any validity, and then immediately jumped into a relationship with someone new (or someone they kept in touch with for just such an occasion) telling that person also that they loved them (even when only a few weeks before they claimed to love their partner), well I’d say it’s pretty clear that the person who broke up was right in doing it and had the other person pegged exactly right.

The OP described the dynamics of the relationship just fine. I had a similar dynamic in mine. I have a qualified point of view. The truth is all you have is someone's word to go on, and not your own assumptions of what they may have, or may not have been thinking when they said what they said at any given moment. For instance if I I you step on my property, and I shoot you in the arm, then tell you to run and never come back, or I'll shoot you in the head, are you going to come back because you're going to assume I'm just saying

How did you know I called her? Did you tap my parent's phone?

Maybe you should put an end to all your life altering distractions, then storm up to them and declare that you're ready to begin again..