Though I have never used a boresnake, the above post are all very valid. Sounds to me like you are trying to pull a "dry" boresnake through the barrel. Try a little Hoppes no.9 or equivelant, then pull like a man, watching to make sure it doesnt catch on anything. Unless you get one for a 17cal. you cannot use the wrong one, obviously you cant drop a larger caliber snake into the bore, the copper part will NOT fit.
Maybe off topic but I make my own snakes, take a peice of heavy weedwacker line, cut 12" longer than barrel. Simply melt the end with a lighter untill you have a glob, let cool, cut the other end at an angle so it is pointy. Take 22cal patches, standard round toothpick and poke a hole in the patch. Slide patch onto pointed end all the way to the melted glob which will hold it in place. Dunk said patch into Hoppes or equivelent, feed pointed end of line into chamber untill it comes out, grab on wrap around hand and pull it through. Replace the patch with a new clean one, reapeat untill patch comes out clean, one last patch with a drop of good quality bore lube and your done.
Nylon string trimmer line cannot hurt your bore, no possible way, clean patch everytime, no dragging dirty anything back through your bore. Most match 22lr shooters will tell you cleaning harms far more barrels than shooting. 22lr is slow and soft, my opinion is a brush is almost never needed. Frequent cleaning with this freebee string trimmer "snake" will probably surprise the heck out of most of you.
I make them up and put them with patches and a toothpick in tiny ziplock snack bags, always ready when you need emm, darn near free if you have a weedwacker.
Hope someone benifits from this idea, I like to pass on free tips.
Enjoy your shooting , Rigby