Robertson has had a tough start to his NHL career having played in just 87 games over of 4 seasons thanks in large part to a number of significant injuries. The 5'9 winger is coming off of the best season of his young career and showed that he can contribute, registering 14 goals and 27 points in 56 games while averaging 11:23 TOI per game. Unfortunately, and even though 13 of his 14 goals were scored at even-strength, Robertson never fully gained the trust of former Leafs head coach Sheldon Keefe, often being the odd-man out when the team was fully healthy and even losing his spot to Fraser Minten to begin last season.
Regardless if he files or not, Robertson still has the option to sign his qualifying offer or continue to negotiate a new contract with the Leafs. If he truly does not want to be back with the Leafs, he can refuse to sign any contract and sit out the entire season, but that is only going to hurt his young career even more.