You're confusing love with infatuation, which happens at the beginning of a relationship but does generally fade off after a while. Love is something different. If you think that true love doesn't exist, it's because you've never felt it. Infatuation is what makes you want to fuck someone and not be able to stop thinking about them. Love is what makes you mourn when they die or move away, or takes all the energy out from under you when they aren't there for a while. It's even possible to love and despise someone at the same time. It will make you foolishly give up your happiness to support a relationship that is obviously sinking and burning, making excuses all the while. It will make you go out of your way to help someone who is hurting at a cost to yourself, and fill you with warmth when you do. This coming from someone who's had two multi-year relationships, one that ended in a suicide after a long spiral and serious errors on both sides, and one that is successful and mutually beneficial, but has its bumps and occasional doubts, like all relationships. It took a long time to tell the difference, because love is a quiet, subtle force that you don't always see until something isn't there.
Infatuation makes you horny and obsessed, but love makes you really care about another person. You can definitely have one without the other, but infatuation is fleeting and shallow, and love is deep and beautiful and painful, and the echoes of a true love never fade, even once it's ended years ago.