Why do some offers use some, not any?

Because an offer expects yes: would you like some cake? sounds friendlier than the real question do you have any cake?

Can any mean whichever one?

Yes, in positive sentences: take any seat you like. That's a third use, different from questions and negatives.

Grammar, compared

Some is for positive sentences and offers. Any is for questions and negatives.

Some / Any
Some	Any
I have some money.	I don't have any money.
Would you like some coffee? (an offer)	Do you have any coffee? (a real question)
There are some apples in the fridge.	Are there any apples in the fridge?

Some and any compared
Point	Some	Any
Sentence type	Positive statements, offers, requests	Questions and negative statements
Example	I bought some bread.	I didn't buy any bread.
Offers and requests	Would you like some water? Can I have some help?	Not used in offers
A third use	Not used this way	In positive sentences, means it doesn't matter which: you can choose any day.

Alguno and ningún both map loosely to some and any, so English asks you to look at the sentence type, not the meaning alone.
Use some in a question that is really an offer or a request: can I have some sugar? would you like some help?
No, ningún becomes not any or no: I don't have any pets, or I have no pets, never I don't have no pets.
Any also means it doesn't matter which, in a positive sentence: you can choose any day. That is a separate, third use.

Why do some offers use some, not any?: Because an offer expects yes: would you like some cake? sounds friendlier than the real question do you have any cake?
Can any mean whichever one?: Yes, in positive sentences: take any seat you like. That's a third use, different from questions and negatives.

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