"In biological terms, men don't choose - they compete to get chosen"
Yes, but no. In some species, females don't get a choice. The male competition plays out and the females are mere booty, so to speak. In other species males compete for mating opportunities, and females choose who they are going to grant their favour to. But in some species there is mutual choice - ie as well as the usual business of females choosing males, there's also males choosing females.
The reason why it's usually females choosing males is that the females are the scarce resource and the males are the plentiful resource - ie a hundred males and a hundred females aren't going to produce more offspring than ten males and and hundred females. So you only get into a males choosing females situation when the males are themselves a scarce resource. And this applies where males are required to put in some resources (ie labour) to keep the offspring alive and kicking. So think pair bonding, eg in birds.
Humans are pair bonders because on average, before the welfare state, a woman couldn't keep her babies alive on her own. This is because of the helplessness of human infants and the length of time they remain unable to fend for themselves - and the consequent burden on the mother's ability to keep herself alive. A woman needed help. So if a man has to put in resources, he's going to choose which woman (of those available) is the best investment.
But even with pair bonding, there's a pay off for cheating. If you are number 14 male bird and you've bonded with no.14 female bird, then it's in your interests to sort out Mrs 17, 25 and 46 down the wood when their husbands are away. Because if you do get Mrs 25 up the spout, you're not going to have to provide any resources. You'd like to canoodle with Mrs 3, but she's not going to give you the time of day, since she's got Mr 3. But watch out, while you're chasing after Mrs 17, 25 and 46, male birds 1-13 are after your missus. You're safe from male birds 15-100, because your missus won't fancy them.
And so we get to all the fun stuff which drives literature film and art - the pursuit of long term mates; and the simultaneous pursuit of something on the side. Where something on the side means different things to men and women. For women it's something better than I've already got. For men it's just "more beans please, miss !"
Humans are clever, complex pair bonders and our behaviour is certainly not deterministic. We have enormous flexibility. But we don't have infinite flexibility. We all have our animal brains, which have been tuned by evolution. So we have instincts to behave in particular ways. We have instincts that exist as potential and which are tuned by social and environmental factors when we arrive and develop in the world. And we have brains that can think rationally (OK reasonably rationally.) But we should not assume that thinking rationally will always and easily trump instincts. It will do so sometimes and with effort.
I'll try a variant of a JP trick on you all. I imagine that pretty much every one participating in this thread thinks him/herself pretty well educated, pretty intelligent and pretty rational. Now go off to a quiet room and close your eyes. See if you can think of ten stupid, irrational things you've done in the last month. (And yes, buying those cookies when you're on a diet definitely counts.) If you have to stay in the room for more than fifteen minutes, because you can't get up to ten - you're lying to yourself.