I am well aware that I'm just speculating but I will explain my thoughts since you asked. I think the contract extension was offered during a time when the team was still doing relatively well. Despite falling behind in the title race, we had several big wins in the first half of the season, and were still going strong in the CL. If I recall correctly, Castles had published talk about Jose being unhappy at Utd and about PSG being interested in his services, which wasn't quelled by some comments that Jose himself made in the press. Put all these together, and I imagine the board believed Jose could still take us forward, and wanted to make a show of faith in him by giving him a new contract. They also got him Alexis Sanchez, known before he came to Utd as one of the best players in the league.
Then the 2nd half of the season happened. Sanchez was used as a LW and turned to shit, Martial was dropped and turned to shit, Rashford played less and turned to shit, Pogba turned to shit, the football in general turned to shit. We went out of the CL in a humiliating display against Sevilla, which ended with some frankly inexcusable comments from the manager about our football heritage and player quality. Persistent rumours of unrest with Martial and Pogba started. Lukaku got injured and the goals, which were already running low, completely dried up. We lost the FA Cup final to a struggling Chelsea side whose own manager was openly at odds with the club and who failed to finish in the top 4. There were still some major positives, e.g. the grit and quality that we showed showed in beating all of the other Top 6, and we managed to secure 2nd place. But I would say that the 2nd half of the season is when some really big question marks over the manager started to creep in, and it's not impossible that the board's faith in him was shaken as a result.