There are a lot of men who would probably say that desperate is an exaggeration especially if they can get sex whenever they want. It is true that men are more likely to have sex as compared to women. They find it harder to control their sexual impulses so they are more likely to be tempted especially with people who are trying to seduce them.
There are some men who would push you to have sex because that is the only thing that they want from you. You may want to determine first if the man that you are dating is sincere or would only like to have fun. Some men are known to leave women after they have gotten what they want.
The short answer to this is that if a man feels horny and he has no partner, he might well get desperate for sex. But you say 'men' as if the explanation for one man's behaviour is an explanation for every single man's interest and longing for sex. The sex drive is very much higher in males under forty than after this, but again, this is a generalisation that doesn't always hold.
Believe it or not, there are some men whose sex drive is quite low and who may be content to go months without sexual gratification. If, however, you have been turning a man on and not allowing sexual activity, he might well be acting 'desperate'