I've always loved this album, but understand why it's so divisive.
This was the first Genesis album I heard from beginning to end, and that may be why I regard it so affectionately. It was 1985, and I hired the cassette from the local library, having heard some Genesis on the Radio 1 Friday rock show. I had heard Dance on a Volcano, but I didn't have enough 'pocket money' to buy A Trick of the Tail. ATTWT was the only Genesis album they had in the library.
Down and Out caught my attention straight away, which it's driving 5/4 back beat, heavy bass and rich melodies. Burning Rope and The Lady Lies were sufficiently proggy for me to enjoy and to relate to the stuff by Rush, Marillion and Yes that I'd recently heard. The softer songs like Undertow and Many too Many also pleased my ears, purely on the strength of the melodies and the emotional impact of the lyrics, notably for Undertow.
It's a flawed album. I can appreciate that now, having explored all their albums repeatedly over many years, but it remains in my Genesis top 5 for personal reasons. We all have a 'soundtrack to our lives' and this is part of mine, as it meant so much to me in 1985. My father was terminally ill, and I just remember walking home from school on dark and cold afternoons, listening to ATTWT on my walkman. The music took me somewhere else, away from the trauma of what awaited me every day when I got home.