I'm trying to build a custom Bard subclass right now, and I just noticed upon finishing the first version that I can't publish it on site since it says it's "This homebrew Subclass has data mapped to it that is licensed content or private homebrew. This typically occurs when licensed or private homebrew spells are linked to the Subclass."

I'm not sure how this is possible as I built the subclass from scratch and made sure to only include spells from the 2014 and 2024 "core" rules and not the PHB. Unless of course there's some overlap there or something?

Here's all the spell content this class uses (it doesn't include any additional homebrew content, again it was built from scratch):

Ray of Sickness
Command
Disguise Self
Scorching Ray
Hunger of Hadar
Major Image
Evard’s Black Tentacles
Hallucinatory Terrain
Geas
Mislead
Poison Spray
Ray of Enfeeblement
Arms of Hadar
Blight
Chill Touch
Darkness
Entangle
Grease
Hellish Rebuke
Inflict Wounds
Summon Fiend
Wall of Thorns
Fire Bolt
Fireball

According to the spell picker, all of these are part of the "core" rulesets for 2024 and 2014, and apart from these I don't have any other content tied to my subclass - everything else was custom written. What's going on here?

It's not about whether whey are core rules but about whether they were part of the Free Rules. 

For example, the 2014 Ray of Sickness is not free but the 2024 Ray of Sickness is free. Neither the 2014 Hunger of Hadar or the 2024 Hunger of Hadar is free.

Here are links to the lists of free spells:

Link: 2014 Free Spells

Link: 2024 Free Spells

Anything not on those lists will be considered licensed and prevent publishing.

Reminder: you do not need to publish homebrew for you or the members of your campaign to use it.