So this has certainly never happened before... The fridge simply doesn't have the option to feed the baby. It's not a custom fridge, it's also not a mini fridge (though I do have the any food from mini fridge mod). Any idea what could cause the interaction to not appear?

Hmm...
Do other options even work? I've never heard of this. Which fridge? I don't know if it helps to know what fridge it is, but let's try.
Is it a baby or a toddler? Maybe if it's a toddler you can feed it with Smart Milk in the meantime. You did say baby, I just want to clear that out.
Is the baby in another room or in a crib or something? I did find this thread on Reddit in the Sims 2 subreddit. Perhaps it can help?

Have you made sure the sim is a parent, sibling (teen), grandparent, lives in the house (visitors can't, even if they're direct relatives), or should otherwise be capable of feeding this particular baby?

Do you have any mods that could be conflicting with bottles/baby feeding?
- Could babies be fed the last time you had babies on a lot?
- Have you added new mods since?

Can the fridge be interacted with normally otherwise?
- Can you get bottles for toddlers, or are only infant bottles affected?

It doesn't appear if the baby is asleep, or otherwise unable to be interacted with, and only appears for family members and the nanny.

Other options appear as they should, and they work fine. I tried with many fridges yet none of them had the option. It is an infant, yes, and his crib happens to be in the kitchen/living room area. He was in Jennifer Burb's arms when I first tried to feed him, so it's not that either.

I found that reddit post as well, though unfortunately that didn't help either.

- Yes, I had both parents try and feed him.

- As for mods, I have the no baby harassment mod but I never had this problem with it before. I think I also have BO's Butler Is No Nanny, but I'll have to check. I think I'll run HCDU later just to be sure.
- I'm playing with the Burbs now when this happened, but I think this happened with Brandi's new toddler too (not Beau), yet the option appeared again shortly.

I am aware of all that. The baby wasn't sleeping and his mom was being held when I tried to get the interaction to appear on the fridge.

If its just this family try forcing error on the sims or even resetting them by deleting them, saving and reloading the lot. I had a family a couple of days ago that had an error and then options stopped showing on the fridge. Rebuying the fridge (something to try) didn't help but forcing error on the sims did. The game can have random glitches.

Ah how come I didn't even think to try that?? I'll have to try that the next time I open my game.

What does "his mom was being held" mean?

If the Force Error doesn't work, something this weird is likely to be a mod conflict or piece of bad CC. Remember, it doesn't have to make sense at the human level! You can try to shortcut the process with the HCDU, but there may well be a 50/50 in your future, and it won't be as bad as you think it will.

That was a typo, my bad.. I meant that the mom was holding the baby

Yeah, I think that's likely as well. I'll try forcing the error first and then run HCDU if that doesn't help.

Edit: I "sold" both the baby and Jennifer with moveobjects and reloaded the lot, and it helped! I don't know why I didn't think of that earlier so that's entirely on me. Thanks for reminding me though! No social worker today!

Sometimes the weirdest glitches turn out to have the simplest solutions. Bravo for solving it! :D