From what I understand it is as often a problem with translation as it a clear political standpoint. What makes the phrase 'mainland China' problematic in English, is that it can mean a number of things. Someone from China using it may do so because:
* They were taught to do so and simply understand it to mean 'someone from the People's Republic of China'. No political subtext intended.
* They use it to mean that they are from the literal mainland of the People's Republic of China, but not Hong Kong or Macau.
* They use it because they genuinely see Taiwan as 'that other part of China' that needs to be unified with the People's Republic of China, despite having been a sovereign democracy for over 70 years.
When you say "I am from China" (or "I am from the PRC"), there is no chance of this having any deeper political meaning. When you say "I am from mainland China", there is a good chance that you do see Taiwan as a 'rogue province' and may support its 'inevitable' reunification by any means, including force. That latter sense is the one that is highly political and irks many people.
Note: there is no need to get into the justness or wrongness of Chinese reunification here; it would be off-topic and not likely to be fruitful. I do think it is important that people understand that the phrase 'mainland China' is not bereft of connotations and may cause readers to form an opinion of the person using it that may not be in line with that person's actual intent.