You understand how present value works right? Holding a loan on balance sheet generates a stream of income that extends into the future and has to be discounted and have credit value adjustments applied, which is very expensive because you have to then hedge the rate and credit risk on top of funding the actual loans themselves. Selling a loan has two benefits over this. Firstly it generates actual cash now which you can book right away and is real so doesn't need to have CVA and discounting. Secondly it gives you a mark to market price for any piece of the loan or similar loans which you are still holding in your book.
I'm not speaking theoretically here - I have been forced to sell loans for capital reasons because they were too expensive to fund even though they were all current, 100% money good and massively overcollateralized.