The expression of 「必ずしも + negative word 」means, not always(necessarily) so.
1.運動をよくする人が必ずしも長生きするとは限らない。translated into English,
People who exercise well do not always(necessarily) live long..
You can also say, or write
2.運動をよくする人が必ずしも長生きしない。It is the same meaning as above.
People who exercise well do not always(necessarily) live long..
The difference between 1 and 2,
1 uses 「限る」verb, which is [be limited ], it emphasizes the case of the longer life without exercise well more than 2.
We have more similar expressions with 必ずしも, 「必ずしも~わけではない」when you describe the reason and feelings. It implies it can't be helped, its something like that.