Why does anyone compete? Those who do believe the person or object is a worthy prize, and the more people want something, the more its value goes up. It doesn't make someone less intelligent or weird to want someone wanted by others.
We judge each other everyday by how many people want us or others. So, competing just takes it farther by saying, since you're so valuable to more than one person, I think I like you, and want to fight for you, to see if I have a chance of winning your affections. In other cases, some people just like to win, regardless if the prize is a good one.
Humans are competitive by nature. Survival of the fittest. Whether it's Tarzan knocking his chest to yell higher than all the other apes to prove to Jane, he is superior man, or a guy who likes a girl, working hard to build up his physical, social, and sexual abilities so that he can be seen as a superior option compared to the person's competing for his crush's attention, it's the same principle. Also, people tend to want that they think maybe out of reach. If they work hard for it, fight for it, they feel it's more valuable. If it's easily had, they think it's not worth as much.
Same concept of competing for a dream job. You do your best to stand out as the perfect candidate or partner (in terms of dating and relationships) so you will be the one chosen.