I can't speak for everyone, but you are probably being downvoted for two reasons:

1) Apologia does not meet "I'm sorry". Read the first few sentences of the article for an explanation.

2) I shudder to think of a world where everyone felt the only criteria for whether it was all right to do something was legality. We should all be grateful that most people don't go through life with that mindset.

The first sentence in the article: "About the title Many people were misled by it, and this wasn’t my intention. I was merely alluding to the book by Hardy, A Mathematician’s Apology, which spent time explaining and justifying his life as a mathematician. (Hardy, in turn, was alluding to the Apology of Socrates. It’s an apology in the classical sense (an intellectual justification), not an expression of remorse. My mistake - as a math geek, it’s easy for me to forget that most people have never heard of Hardy."

"Apology" doesn't necessarily imply remorse, just explication.

Legal and Ethical are two different things. Confounding both, in the eyes of people is Understanding.

It may be legal to something, but unethical. It may be ethical to do something, but illegal. There are many examples of both. The reason for this article is apparently to spread understanding amongst people who think it's unethical to do HFT, but may not understand what HFT does and how it works. By writing this article, he is hoping to convince - via understanding - people that HFT is also ethical.

You have just admitted to not even reading the first paragraph of the article, in which he explains his meaning of the word "apology."

So it's not possible, in your opinion, for something to be both legal and unethical?

It's an apologia rather than an apology.

Are you suggesting that people should only apologize for things that are illegal?