I was a refused a UK DATV visa. How should I proceed?

I am a Chinese passport holder with valid study permit in Canada. I am in Canada now and planning to visit my brother in the Republic of Ireland. (I have got the visa for visiting Ireland) My flight to Ireland is a direct flight whereas the return flight requires a transfer in London, same terminal in same airport.

I researched online and found that I don't need a visa for that flight. I was not sure so I called UK Visas & Immigration and they insisted I need to apply for DATV. Now after a few weeks of application, they refused me, allowing no appeal, and stated in the letter: You have applied for a visa to pass through the UK en route to Ireland, I have carefully considered your application but I am not satisfied that you qualify for such a visa.

How am I supposed to understand this line?

I am really confused about it. But now I can only change that flight to a direct flight, which is more expensive and shortening my visit.

Will this refusal have any effect on my future visa application or entry to another country?

Response to @pnuts: Yes, I applied for it for the proposed return journey (en route to Canada) which is indicated in my application form as well as my cover letter in order to clarify things.

Response to @Gayot Fow: Thank you very much for replying. The date of my refusal is Dec 2nd and I was probably debited from my account at the last week of November. Another question I want to ask is, will this refusal cause me any trouble when entering the border of ROI and Canada?

Update: So I found the complaint webpage online and file a complaint to sent to their email address. I included all my documents as explanations and paragraphs to explain. But their response was simply Your application was refused for the reasons stated on your refusal notice. You are free to apply for Entry Clearance at any time. I feel like they didn't even look at the evidence I provided. I am really disappointed.