To be unbluffable, you would need to call all bluffs.
To ensure that you call all bluffs, since you're not psychic, you need to call every time they bet in certain situations where they might be bluffing.
To call in all situations where they might be bluffing, you need to call every time when they might be bluffing but might be actually holding a hand which is beating you.
This is a problem for a couple reasons. It means, for example, there are stupid extreme situations where they go all in for 40x pot when there's a 0.0005% chance they're bluffing and a 99.9995% chance they're crushing you, and you have to call (else they might occasionally succeed in bluffing you).
Also if they recognize that you're doing this (or even less extreme versions, like you just have a larger than optimal tendency to call when they may be bluffing in some situations). They can easily adapt to exploit you in these cases by betting larger amounts more often when they're ahead of you with unlikely hands (when their range is more likely to be behind your range, so it appears more like a bluff), and by bluffing less often when they are actually behind, but their range is ahead, etc.
Obviously, if you could somehow know for certain whether they were bluffing or not, you would always call their bluffs and always fold to their non-bluffs. This would be the best thing ever for you if you could play poker like this. But you don't know for certain, and you have to make your decisions based on hand ranges, so attempting to be completely unbluffable thus means making calls in cases where it would be unprofitable against their range to do so.
In short, the reason you want to be bluffable is something like that attempting to be unbluffable drives you to play suboptimally in situations where they might be bluffing. If you want another (maybe intuitive) answer, it's because you're assigning some external value to being a correct bluff-caller which is different from the money you're winning in the game, so it skews how you make your decisions. It'd be like you assigned infinite value to correctly calling bluffs when you're trying to calculate your EV.