"What can I do for you?" In this context, it's a slightly rude way of asking, "How can I help you?"

I am a native speaker of English. I don't understand why A considered B's response to be rude.

The only excuse I can think of is that B's question was very direct. A's initial message was very bland (I think it was automatically generated by iTalki, but that's a separate conversation). Usually, English people respond to bland messages or conversation with something else bland; often we will have an entire conversation about nothing - we call it smalltalk. Many English people are shy about saying what they want. Clearly, there are contexts in which we do this freely, otherwise we would never be able to eat or have babies, but in a smalltalk context it is considered too forward to discuss anything important or negotiate anything. This is baffling to most foreigners, but getting to know an English person involves using smalltalk. If A has not met many foreigners before, they may be unfamiliar with directness, and be upset by it. This is a common problem with/for Americans and Chinese.

To me, it’s not rude at all. Especially in this case, where someone sends you nothing but the system-generated message, it’s perfectly legitimate for you to ask what they’re looking for. As a teacher here, I would send a differently-worded message, of course, but as a general rule, people who choose to send unsolicited messages to random strangers have to respect the fact that the other person is also a human being, and may not react exactly as the sender may hope. Frankly, the fact the sender chose to take the response as “rude” says a lot about the sender’s personality. What’s more, the fact they immediately accused the other person of rudeness, instead of giving them the benefit of the doubt, should be a big red flag.

"What can I do for you?", culturally, is an expression mostly used in transactions. As in, a store clerk will ask you this as you enter a store, or a customer service agent will ask this question when taking your call. For this reason, a native English speaker will think of it as cold, because it sounds very impersonal. Also, it's often used as an ironic response to someone who is making you uncomfortable. For example, if someone in a bus stop or in a library keeps looking at you, you might turn to them and ask them "what can I do for you?", meaning to say "either be clear about your intentions with me, or stop what you are doing". Either way, and this is a personal opinion, A's response is rude, considering they had no ground to believe B had any bad intentions.