I realise most women don’t find “I’m horny” a turn on. And “I need to come” is even worse. So why do men say such things?

First, understand that most men would be aroused by hearing such things coming from their wife’s mouth. So he’s just doing unto you as he wants you to do unto him.
The second issue is going to be a lot more difficult. The truth is sometimes he is just horny and “just needs to come”. When this gets strong enough it pretty much overwhelms everything else. If he’s a decent guy he is only interested in sex with you, but the truth is he is seeking something physical far more than an emotional connection.
Because many women are not this way, many judge men for it. But judging him for something that’s a part of who God made him seems rather unfair to me. Sure he can learn to deal with it better, but that doesn’t change his reality. If you expect him to lie for the sake of your feelings, what does that say about you and your relationship?
For the most part, just needing to come is an indication he’s not having as much sex as he would like. Young men may want more sex than is reasonable, which means being in this state much of the time. Beyond those things, sometimes we just get really horny and we have no idea why. A sudden boost in his drive does not mean he’s looking at porn or thinking of cheating.
You can do one or more things with this information:
~ Paul – I’m XY, and I think the last one would be good for your marriage.