Was a really good (and long) article on it for those with a subscription to The Athletic.
How Premier League and EFL works out fixtures: Algorithms, pairing teams and long Tuesday away trips:
The guy who does the fixtures every year seems like he's used to conspiracy theories:
"Thompson is used to being depicted as the dastardly menace out to sabotage clubs and will knowingly roll his eyes at the suggestion of his fixtures being rigged. “Over the years you get used to it,” he said."
They do the bare bones of the fixtures and then questionnaires are sent to every club, who are asked for views and observations on the schedule placed in front of them. That brings the opportunity for feedback, with clubs able to make date requests to their relevant league.
One club might be keen to play away from home on the same weekend a major public event is taking place in their town or city.
Another might also request away games either at the end or beginning of a season, because of planned ground improvements. That was the case with Liverpool in 2016-17, when their first three league matches, taking them up to the September international break, were all away from Anfield as they added the finishing touches to their new main stand. Their first home fixture that season wasn’t until September 10.
The Premier League and EFL will do their utmost to accommodate date requests but offer no guarantees. The EFL, for example, typically receive between 80 and 90 date requests from their 72 clubs in any given season. They estimate about 85 per cent of those get granted.