From Boise Ed, who notes “Total CIDU for me”:
I have a maybe-theory but let’s see what y’all think.
Oy. I momentarily forgot which strip this was from, so I asked Google Images. The AI summary says:
This is a comic strip from the series “Bizarro” by Dan Piraro.
I don’t think so! (Yes, I was able to figure it out.)
Comics I Don't Understand 
His nails are too long and sharp to safely use for contacts?
That was my thought.
Women with long nails can and do put in contacts. The secret is to use the front of the finger instead of the tip. But clearly this strip is telling us dogs can’t put in contacts like that.
I can’t believe I know this. Eyeglasses function as protective goggles while clipping (toe) nails.
I think Brian R has it, although for me the problem with long fingernails and contact lenses isn’t putting them in but taking them out.
I found references on the web to not wearing contacts for manicures because the chemicals can do nasty things. Never having had a manicure in my 64+ years, and not wearing contacts anyway, I dunno.
Keera Ann’s got it. Eye protection from flying nail bits. Had to wear them myself when clipping my dog’s nails. Never put them on the dog though, maybe should have.
My initial thought was the same as Beckoningchasm.
I guess that if dogs can talk, they can deal with contact lenses.