eBay and Paypal are mutually beneficial. Paypal is absolutely reliant on ebay for sheer volume. It's their foundation.
But I just don't think sellers liked being cornered into having to accept PP 99% of the time.
eBay is off it's core market, chasing more lucrative opportunities. Problem is, they don't own that other market (amazon, alibaba), never will, and are pissing off their base with every new change. It's the curse of needing constant growth in our economy.
Well, eBay and Paypal are fundamentally tied together.
eBay is a marketplace, but they don't do payments. Paypal does payments, and more importantly, Paypal lets random joe customer pay with a credit card to random jane seller WITHOUT a merchant account.
That's the key, because Amazon and Google and others are pretty much buyers are regular consumers, sellers are businesses (who may be single person owned and operated, but still has a business entity). Whereas sellers on eBay are made up of several groups, from standard companies to someone who found something in their attic one day. And the latter are NOT able to traditionally get a merchant account, which means they normally could only take limited forms of payment (cash, cheque, money order). Which over the Internet is... a stupid idea (who wants to go out and send a letter, wait a week, blah blah blah, when you can enter your credit card number and pay within minutes?).
Now, the eBay-Paypal split is probably to answer some of eBay's biggest customers (i.e., the people that run whole companies) to allow for alternate payment methods - including their own credit card payment system (or Amazon or Google), to be more flexible. Though you can probably guess eBay will mandate some form of credit card payment must be allowed, even if it means for most joe sellers, Paypal. (Again, because who wants to win an auction, then go out and get a money order by lining up at the post office, then mailing it out snail mail, and hope it gets there a couple of weeks later...).
Paypal has competition in all areas except person-to-person payments (well, they technically do have competition there too if you count bitcoins, but until someone makes it so I can buy bitcoins with my credit card and it magically all works like Paypal, it's a complex option).
eBay has network effects though - competition with eBay tends to be very niche or not at all. Because face it - eBay has customers, and sellers know that. And buyers know eBay sells practically everything. If you want me, as a seller to use something else, you better provide something good (usually in the form of lower fees). If you want me, as a buyer to use something else, you better provide something good for me (usually in the form of lower prices).
But there's a mismatch - buyers don't want to pay eBay prices off eBay, and sellers don't want to sell for much less than eBay because they'd just list on eBay instead. So sellers complain buyers "lowball" bids, while buyers complain that sellers ask so much it's just easier to stick with eBay.