Sporting president is making one mistake, which is going back on his word, otherwise asking for a lot of money isn't really wrong at all. If he just came out and said "hey , I want 100 million, that's it" and that was the last of it, then anyone who paid 100 million would get him, that is even more than right now, and nobody could say anything, Gyokeres is a player under contract and the team decides how much they want, end of story.
The issue was, Gyokeres and Arsenal worked out a deal, where Gyokeres and even his agent is making less, just to make sure this deal happens, and Sporting gave a number, which everyone worked towards, but then, Sporting wanted more, and that's the real issue here. If you give a price, you stick to that price, you do not change it higher when that price is matched, that was the bad part of this deal.
Until a few years ago, Sporting was irrelevant in the Portuguese league. They weren't winning the league. Gyokeres came and helped the team win titles. With his departure, Sporting returned to being the shitty team it was before. They only managed to sell players, but they couldn't win anything. I see that Sporting's president is afraid of returning to the old days when they were irrelevant, which is why they're focusing on creating numerous obstacles in the player's sale agreement so that Arsenal backs out and Gyokeres stays at the club.
Gyokeres also doesn't want to stay at Sporting, even if it means not playing and facing disciplinary proceedings. The president of Sporting knows that even if Arsenal paid 100 million or 200 million or whatever amount of money it was, it would not prevent Sporting from returning to the old days of failures, only if Gyokeres stays and plays and Sporting would be saved and of course his position is also at risk if Gyokeres leaves because when Sporting starts to lose a lot like in the old days, he will be seen as guilty.