Why can't I buy a Bitcoin from an online service using Paypal?

Coinbase wants my bank account info - which I am reluctant to give them.

Paypal would limit my exposure.

Thanks in advance.

My wag is that Coinbase (which I never heard of) doesn’t want to pay PayPal’s commission fee.

That is plausible.

Someone else told me Paypal is not reversible - which scares me about a bank account that is so.

Because legitimate financial institutions are worried about exposing themselves to money laundering charges among other thing financial crimes. The reality is that bitcoin, and other virtual currencies, have less utility as a real currency than as a means of conducting illegal transactions and avoiding taxes. Paypal knowingly facilitating that would make them liable for little to no upside. Just look what happened to the BitInstant guy.

There is also that fact that bitcoin does many of the things Paypal get paid to do. So there is no reason for Paypal to hasten their obsolescence by supporting their “competitors”.

There is another, more practical reason - fraud on the part of buyers. Even individual Bitcoin sellers were wary of accepting PayPal back when Bitcoin was new. It was rare to find someone willing to sell their BTC over PayPal, and they often charged a higher ask price for it.
PayPal transactions are in fact reversible. That is not good for the seller when purchasing a fundamentally irrevocable item. The buyer can falsely claim their account was compromised or the purchased items were never sent, while the buyer keeps the BTC and the seller’s money taken back.

There is also the matter that current PayPal policy does not permit using the service to buy or sell Bitcoins or Bitcoin-related items, under threat of account closure.