@cappellof This will depend on the rear cogs as well. If you're in large in both front and back (or small to small), this puts the chain at an extreme angle, known as cross-chaining. You generally just want to avoid those gear combinations. Even a perfectly adjusted bike might still rub when cross-chained. That would more likely rub on the inside of the cage, though.

Since your's is rubbing the outside of the cage, you probably either don't have enough tension on the cable so that it's unable to pull the cage far enough, or the high limit screw is preventing it from moving further. To check, push on the lever to try shifting up even though there is no further gear: does the cage move a little bit further? If not, the limit screw is too tight. It should be labeled with an H on the derailleur body, loosen it a quarter turn at a time until the rub stops. If the cage DID move, then it's probably the tension. Rotate the barrel adjuster by the shifter counterclockwise to tighten the cable, again quarter turn at a time.

Lastly, it's possible the angle of the entire derailleur cage could be slightly off, but I'd say that's unlikely.

Park Tool has a great video on this (and lots of other adjustments too) https://youtu.be/ZNG7g83lI-s

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The majority of front shifting problems can be solved with basic adjustments to the limit screws and index setting of the front derailleur system. In this vi...