I am taking BJJ at a self defense (as opposed to sport) oriented school-Gracie Jiu jitsu.
It seems to me that when someone is in my guard (if I'm using the term right), when I'm on my back with my legs wrapped around their hips and their head hugged down next to mine with my right arm wrapped around their head and my left hand on their right upper arm, hugging them close, that I am very vulnerable to being bitten in this position in a streetfight- it would be very easy for the guy on top to bite my neck, shoulder, chest, etc..

Any thoughts on this? am I wrong?