Where did you hear this from? Personally, I think it's safer to use the same address more than once, since you already know that you can successfully deposit it.
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By saying each address shouldn't be used more than once, it actually means if you're spending from an address, it's good practice to empty that address and never use it again. Receiving multiple transactions from one address is fine until you spend with it. This used to be more common advice, but like what other people already said, it's not very relevant if you don't care much about privacy (which you probably don't have if you use centralized exchanges).

One more somewhat minor reason why address reuse can be considered bad practice is that future quantum computers can possibly hack into addresses that have already been spent from because their public key has been exposed. Not very relevant, but probably worth keeping in mind.