Why other mobs can still attack me after drinking the potion of invisibility?

According to the wiki, here is what a potion of invisibility does :

Makes player model disappear and mobs will act neutral towards the player if the player is not wearing armor (leave chunk to perform).

So, to use one successfully on solo, you have to :

• make sure you are not wearing any armor
• have changed of chunk

You might now be asking, "What is a chunk ?"

A world in Minecraft is divided in segments of 16x16x256 blocks, called chunks. Each chunk is loaded independently, and sometimes you have to leave the current chunk to force a few things to refresh, such as the mobs comportement towards you.

More info on chunks here.