Why do people say don't mix wine and beer ?

Probably because of hangovers and risking puking the next morning. 

Too much wine makes you feel like sh*t.

Honestly too much beer too or liquor.

I like to mix all 3 but know my limit.

wine then beer seems to cause a high level of dizziness for me, but that doesn't stop me.  

It is an old saying that advises against drinking wine and beer on the same night. It is far from known if it does cause bad hangovers. 

Because the next day, you can be the sickest you've ever been. And it continues into the following day. 

Because they're morons. Be happy.