This also happens with other quests to (Not all of them but some of them). This is a common bug. The best thing you CAN do is to:
1. Wait for a patch.
2. Restart the game from the beginning, but delete the saves first!
*3. If this still occurs you MIGHT have to reinstall the game and have the latest patch installed.
Now if one of those methods work. Make sure you have PlayStation Plus or a USB device and backup your save before you leave Vault 111
* DO NOT choose this option unless the other two options don't workout.
Honestly, pal.. The companions system in this game is literal Ebola... My suggestion is to just use someone completely different for the time being until Bethesda can fix it somehow. Preston is one of the worst, but some others are pretty broken as well.
And yes actually, they DID fix it on PC... A random group of modders fixed a problem with the game WAY before the DEVs did, lol.
Modding+1!