That sounds like you're confusing parrying with blocking. To block a blow, you're meeting it's force and holding it back. That's where you'd need either a strong and sturdy weapon, or better yet a shield. To parry a blow, on the other hand, you're just turning it aside, re-directing its force so that it doesn't land where your attacker was aiming. That can be done with a much lighter weight weapon, and is the primary means of defense in a Japanese swordfight.
And a well-made katana is actually quite strong. In order to take a really sharp edge, however, that edge is honed thin enough that is becomes quite delicate and easily nicked. Although the weapon wouldn't be likely to shatter or snap if used to block a blow, significant damage to its sharpened edge could still ruin it. Though really small nicks can sometimes be mended, a major gouge out of a sword's edge cannot.
