This is purely my opinion and reading between the lines. I think when Wilder was appointed both parties agreed on the way things would work, it seems it's a 'recruitment committee' that makes the decisions on the transfers. I feel the first window in January maybe things didn't go to plan and it caused some friction possibly the 'committee' agreed on player A or B but ended up with player E, which was the start of the rift. This may also of had Wilder wanting to take more control of transfers (he was manager not head coach, us now employing a head coach rather than a manager could indicate this). With the cup run it also got his name in the headlines again and judging by his interviews he isn't short on confidence and thought maybe this could be his opportunity to rather get more control of transfers or move to a prem club. When his name got mentioned for the Burnley job the club could of asked him to come out and say he wasn't interested but he used that to get guarantees in the transfer front. From that point though especially with the downturn in form and the rumour mill in full swing the club could of felt like it was being held at ransom(you also need to remember Wilder was probably one of the first main decisions in the Scott era, and his reputation was in ways linked to how successful Wilder would be). Come the summer by reports Wilder wanted players to make an instant impact but the club was following a transfer model of buying player with a future resale value (which I think Scott was brought in to oversee, after the club lost a few high cost players for free over the last couple of years) and making use of the academy(Carrick has mentioned several times he is a big fan of giving young players a chance "if they are good enough they are old enough"). In interviews you could see and hear Wilder getting more and more frustrated. At that point the relationship was virtually irreparable but Wilder wouldn't walk and the club was reluctant to sack him due to financial reasons so the club and Wilder was at a standoff to see who would blink first. It probably came to a head after Wilders last match and the club's poor form and Wilders refusal to change things. The meeting was probably something along the lines of Wilder blamed recruitment and his system worked it was the players at his disposal which wasn't up to standard, but the club told Wilder he has players at his disposal he isn't using and he wasn't trying to change things to get results. So the club made the decision to terminate his contract(could of been an argument and something was said or something new came to light about Wilder asking his agent to look for another job for him etc etc). What springs to mind for me and is that both Wilder and Warnock both had things to say about recruitment and both would be considered "old school" managers, we have replaced them with a head coach which is an indication of the direction we are wanting to move and fits in with the way the club is progressing with a director of football.
This is all obviously just my opinion, educated guesses, reading between the lines and some pure guesswork, but this is my take on the situation.