Is it a problem if he doesn't hold your hands?

So, I've been dating this guy for about a month now. He's not my boyfriend, but I think it'll eventually progress into a relationship, since we keep in touch every day and tell each other about our days, and we're cautiously starting to tell some of our closest friends about each other (well, I've told my best girl friends, and it seems that some of his friends already know about us... One of our mutual friends hinted to me that he knew about us as well)

He's wonderfully affectionate without being inappropriate, we kiss and hold hands and all that stuff in private. But when we're out on a date, he's never held my hands yet. We still walk very close to each other, and at the end of a date, he's happy giving me a goodnight hug and a kiss in front of my apartment. But my friends thought it was weird that he doesn't hold my hands in public. Is that really a problem? It doesn't automatically mean that he's embarrassed to be seen with me in public, does it?
Is it a problem if he doesn't hold your hands?
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