Yes condoms can be too small (and too big), that's why they come in different sizes.

1. The important thing to remember is a foot of an arm has a core of bone surrounded by a (roughly) cylinder of muscle, whereas a boy's tally-whacker is pretty much just spongy tissue inflated by blood.
Sometimes just the slightest additional pressure in the wrong place or the wrong way can stop a boner; alternately it can cause a guy to "go over the edge" after only a few seconds.

2. Another thing, a wrong sized condom can slip off (or rocket off just like an over stretched rubber band on a tube). Also, if a condom's too small it might not contain all the fluid properly.

3.Finally, some people have latex allergies and so they have to use vinyl condoms which pretty much don't really stretch at all.

So, yeah he could be lying or he could be trying to tell you something about how his body works so maybe have a conversation before you "run so far".

tl;dr

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Hey, at least you can't put a Condom on backwards