Ur not missing anything.Its just that u messed up by considering more than one reference frame at a time.
Pont 1: if u go off on a rocket, then who said that u dont age ie. stay young?? With respect to you ie taking
you as the reference frame you do not age or atleast do not "relativistically" age.But for a person seeing you, you definitely age.
Pont 2: Seeing the other way, if u see them then they age and u dont appear to age.If this does not clarify then see this example:
A hunter (who knows some physics) wants to catch a lion.He sees a lion standing 100m away from him.He thinks too much and this is what he does.He runs directly away from the lion.Now wrt to him, the lion is running away.SO he thinks that it must eventually get tired, lose its kinetic energy and stop after a while which will make him easy to catch the lion.But what happens is that he runs => he loses his kinetic energy and stops..so to him it appears that the lion loses its kinetic energy and stops.But he got it wrong in the last part.Now the lion must come of its own accord to him and be caught, because in the last part: "
will make him easy to catch the lion" he changes reference frame to that of lion.But in essence wrt to him he is still so it must be the lion which must come to him.