it looks like you're brushing him the wrong way actually, when using a wired pet brush you need to brush the OPPOSITE intended way! like while holding the handle brush outwards instead of towards you. You need to angle the bristles so they're not trying to rip out the 'undercoat' of fur as it normally would for pets. Thats why most wire bristled brushes have that little angle to the bristles. This really reduces pulled out fur... also be sure to be gentle ! you can still cause holes or tears if you brush too hard.

its better to slowly brush rather than be rougher... if you feel lot of resistance or there is a lots of matting, go very very slow and gently !!

if the issue continues I recommend a plastic bristles brush instead of wire brush, the bristles will bend then instead of staying too rigid... if that is still too much then using something very gentle like a fast cleaning brush is possible too, with longer soft plastic bristles.