“You too” is an acceptable response to “See You Later”

I don’t know why so many people have been on me about this but I have been so lost on what to say to someone who says “see you later!”

If I say “bye” or “ok” to them in response, I get a questioning look like they’re trying to figure out if I’m angry at them and have even been asked if I’m mad at them for such a short response. So I’ve defaulted to saying “you too” because logically it’s the most appropriate response. But every single time I say it, the other person stops in their tracks and looks at me like I’m insane, and some even go so far as to question me about the response before leaving. Here’s my reasoning:

See you later, in the physical sense, it would be incredibly weird and inappropriate if they only saw me and I didn’t see them. That would be stalkerish. If you’re trying to see me later, it should be in a setting where I can also see you later? So that’s my go to response when people stop and question my phrase

“wouldn’t it be weird if you saw me later and I didn’t see you?”

In the emotional sense, in my head, they’re really wanting to say “I want to see you later” which has been shortened due to the establishment of the emotional connection and implied future repeated reconnection. To which the appropriate response would be “I want to see you later as well” which we could also reasonably shorten down to “you too”

Is that the wrong assumption here? What are you supposed to say when someone says “see you later?” If “bye” or “ok” makes people think you’re being short with them? It just throws people every time I say it but nobody gives me a good alternative answer to what they would rather hear in response.