reckon

it's a VERY tight fit on purpose,...and,....depends on the quality of your clips/pedals, good quality clips/pedals have the strap slots machined and then deburred or filed.
on cheaper models (like MINE) usually the slot where the strap fits through is stamped, so there are sharp edges and burrs (which get smoothed down with leather straps over time) so take a womans diamond nail file (or better: a round or oval rat tail file) and knock down the edges of the slot a bit (if you have a burr quick tool use the fine tip), then bend the strap a little so it humps up in the middle and stick it through the hole as far as it will go (not very far), then as suggested use some pliers and pull them through all the way: it'll still have that hump in the middle where the strap passes through the clip/pedal, thats so they don't slip much, which is why I wouldn't file it or use a dremel to make it any larger.

if you didn't knock the burrs down before doing this, and you have woven nylon straps,(or cheap leather straps) you just shredded the edges of your straps all the way down, and technically they could unravel and fail, although I have never seen it.