I can't transfer ps3 game to ps4?

It probably worked with Destiny because he got the cross-buy version before it expired for that option. The other one is because it's PS3 ONLY version, NOT a cross-buy, and CANNOT be downloaded to PS4. So if you want the PS4 version, you'll have to buy it yourself.

Also, just a warning, what you're doing (or attempting to do) is called gamesharing which is against Sony's ToS and can get your and their accounts banned if they found out.

The PS4 is not a PS3 - it's a different system. This is like asking "Why won't my 1972 VW engine fit into my new Golf? They're both Volkswagen!"

Idiot there's a reason they create new games for new systems.