Saúl is being sold because of a variety of reasons.
1) He's lost his spot as an undisputed starter. This is the main reason for the player wanting to leave Atlético. It happened during the past season because of performances that haven't been good enough. He doesn't have any problems with Simeone - it's the other way around. Simeone has given Saúl the chance to redeem himself on many occasions over the past 2-3 seasons despite the rather poor performances. He's not played well for the past 2-3 seasons but Simeone's always given his full trust. The other reason is the explosion of Llorente who was fundamental to Atlético's league win last season. He's been left behind in the pecking order by more or less everyone he competes with for a starting spot. The club and Saúl have a special relation because of his status as a youth team product which is why they won't stand in his way.
2) Saúl is a rather special case. He's an incredibly versatile player and this is a major advantage when the team needs it for several reasons. He can play LB, LWB, CB, DM, CM, LM, RM, SS and it's something Simeone has utilized to a maximum in order to strengthen the team whenever they've needed it. Saúl is very unselfish in this sense - as long as he plays. But..there's another side to things and that's when he doesn't play. That's when the issues start. He wants to play all the time - even if he doesn't perform. That's also when his entourage come into play and start pressing for more playing time. It has happened in the past - several times - and it'll happen in the future if he doesn't play.
Saúl's biggest problem is a different one though. It's the fact that he doesn't have a fixed position. He's a box-to-box midfielder naturally. He's a goal scoring threat coming undetected from the second line of attack (similar to Gerrard/Lampard) but that position doesn't exist at Atlético and he's not good enough to play as a SS because the options upfront are simply much better. He's very good in the air, shoots well from distance and very physical. He covers tons of ground. His ability to drive the ball is also very good for a player with his technical ability - which is limited and why he can't play as a deep lying DM who'll start play with his passing. That part of his game is very limited compared to the elite in European football. He's much better utilized further up the pitch but he can anchor the team defensively in many games - just not against the best teams if he's supposed to perform that role.
A great player tactically if utilized correctly. He's a fantastic professional btw. I've seen it myself while at Atlético's training sessions in Majadahonda many times.
Most important of all: Saúl needs a change of scenery in order to find himself again. Especially since he's gone through a rough time in terms of mental issues in the past year or so. It'd be good for him and for the club. That leads us onto the next point.
3) Saúl is in the second echelon of earners at Atlético. This is why the club think it's better to sell him with everything else in mind that I've posted about his situation. He's currently player 11-14 in the pecking order but earns a salary which belongs to someone who should be an undisputed starter.
There's also a side story regarding his wages where the club had planned on improving his contract but the pandemic and his performances have come in the way of this.
