I usually use an analogy to explain this. Tracking via first party cookies is like walking into a store that uses security cameras. I have even seen boards that inform the visitors that the store is under surveillance. Generally, the security camera is only monitored/used by the folks running the store.

Third party cookies are like as if the security camera is monitored and used by a random third party company who you are not even aware of. This is why it is bad.

Perhaps we should have a standard badge/button to indicate first party and third party tracking - something like https://www.safetysignsupplies.co.uk/images/product_imgs/ful... for first party cookies and a more "evil" version for third party cookies.