I dislike sites with dark background. Maybe it is a problem with my poor quality LCD screen, but I switch to reading mode on such sites (so that the background becomes white) because they are hard to read.

I'm pretty much the exact opposite. I typically use my computer/phone in a low light environment (monitor and phone are almost always on lowest brightness settings), and a white background hurts my eyes. I use a dark background wherever possible, especially when reading ebooks/longer articles on my phone.

Any good software designed for reading should have good support for both.

Conceded.