Why does the Room of Requirement connect to the Hog's Head instead of the school's kitchens?

In those circumstances it didn't make a bathroom until the girls thought it would be nice for them to be able to wash up. So it was definitely being influenced by the students hiding within it.

So that being the case, if you were hiding out in the Room of Requirements while unsavory Deatheaters were roaming about - would you be thinking of the Hogwart's kitchens? Or would you, I suggest, be thinking of that one pub in Hogsmeade where the proprietor wasn't any too particular about which strong beverages he served up to anyone, regardless of their age ...?

I feel that the Room of Requirement (ROR) took into account the past wishes of the user. For example, Neville had asked for no Carrow supporters to get in

You’ve got to ask it for exactly what you need — like, ‘I don’t want any Carrow supporters to be able to get in’ — and it’ll do it for you!

With this wish already in place, the ROR looked for options of places Neville could get food. The Hogwarts kitchens were run by house elves, which were probably told by the Carrows or Snape to report anything that should not be happening, like Neville hiding in the ROR. Next would be the Three Brromsticks, but since it is so popular, it would make sense that the Death Eaters around and in Hogsmeade would be visiting it for a drink every now drink then. Also, Rosemerta might turn in Dumbledore's Army to the Death Eaters if she feels that her personal security is being threatened. We don't know enough about Rosmerta too make a good guess about her character. I don't know any other places of a reliable source of food that supplies the necessary nutrients for the human body.

So that leaves the Hog's Head, which not only is a relatively unpopular pub, but the owner is also Aberforth Dumbledore, the brother of Albus Dumbledore, so he would also be one of the least likely people to turn in them. Keep in mind that we can justify this, unlike Rosmerta, because he invites Harry, Ron, and Hermione into his pub when the Death Eaters were looking for them. He also covered for Harry's Patronus, so that has to count for something.

With the inferences above taken into account, we can conclude that the Hog's Head is the most likely location that the DA could get a good source of food, while staying safe from Death Eaters and Carrow supporters. That's why the ROR choose the Hog's Head.

Also keep in mind that this was the best way for Rowling to introduce us to Aberforth Dumbledore, someone she was hinting at when Harry goes into the Hog's Head and thinks the bartender looks familiar, so it might not have to do with the ROR at all.

I also think this means that Snape could get in, because he necessarily did not support Voldemort, as he was always with a Dumbledore. Just something I thought of while writing this.

I think the Room gives what the user needs even if it is not fully formulated like Harry finding a whistle by just thinking about needing one but not specifically thinking about asking the room for one.

By that point Hogwarts was not safe and Neville might have had a subconscious desire for outside help and the room provided the one person who could help them no matter what.

the Carrows realised that Neville was the main ringleader and decided that Hogwarts could do without him. Fearing that they may kill him, Neville made for the Room of Requirement, which he was able to turn into a hiding place for the D.A., and to connect to the Hog's Head in order to get food from Aberforth Dumbledore

https://harrypotter.fandom.com/wiki/Neville_Longbottom#cite_ref-DH29_48-0

Or it might be that the connection always existed and the students just didn't know about it: after all it does not make much sense to get a tavern next to the school run by your genius brother who you hate and makes you look daft in comparison.

Aberforth and his brother had a strained, often acrimonious, relationship most of their lives. Aberforth was resentful and bitter about the fact that he was living under Albus's shadow due to Albus's superior magical capabilities and spent most of his time caring for his sick younger sister, Ariana. Albus and Abeforth relationship