An easy mistake to make.
You can see clearly that what your client wants is deficient in some way and you have the right answer at your fingertips. If it’s something related to the design of the website and it’s not a show stopper, let him have it.
My experience is that all you end up doing by inserting your sensible improvement is upset the client. Even if you get your way, there is still residual resentment. It’s a little thing he thinks he got right and you got wrong.
Even if you win a couple of battles, your client will declare war and you will definitely lose.