Hello Andrea!
Sorry for the incomplete answer the first time. Been using Flash for over 20 years and sometimes I assume that things are obvious when they actually are not.
Graphic and Movieclip symbols have different properties and behaviours. Check the documentation to get familiar with both, but generally speaking, in non-interactive animation we use Graphic symbols. Movieclips can be manipulated and controlled by code and suit interactive projects better. Interactive projects can have combinations of both, while in non-interactive projects, esp. the ones that will end up as rendered video (MOV, MP$), animated GIFs and so on there is absolutely no need to use Movieclips unless you really have a reason to.
Since you initially created your symbol as a Movieclip and then possibly put it on Stage and animated it somehow - maybe with a few Classic Tweens - you will need to find each of those symbol instances on the Stage, click on them with the V-tool and in properties panel switch them to Graphic. Each instance on each Keyframe.
(If they are on their own layer, it could be possible to lock everything else but this layer and use Edit Multiple Frames to do it in one go.)
When they become Graphic, the looping section below will change and you will have 'Loop' (most likely it will default to 'Loop' when you switch to Graphic).
It wouldn't hurt if you switch the type of the symbol itself in the Library as you show on the screen grab, but is not necessary.
When all Movieclips on your timeline are Graphic and you have them 'Loop', you may run into sync issues (because you have the keys created while they were Movieclips). Now I'm just speculating, but it is not uncommon. If you have a 12 frame animation inside the looping symbol, but you have a key at frame 7 on the main timeline, the animation will reset on frame 7 and start from the beginning.
To fix this, select your layer with the tween and choose 'sync' in properties.

Hope this helps!
NT