I would hope someone who claims to love me would support my efforts to improve my health.
If I started bike riding to get more physically fit would that be a "threat" to the relationship? What if I decided to eat more fruits and vegetables? What if I joined a walking group (that my partner doesn't care to join) and some of the participants are, God forbid, men? What if a couple of the men are attractive, would I be expected to quit the group to appease my partner?
If my partner views me getting emotionally, mentally and/or physically healthy as a "threat" to our relationship they'll likely not be my partner for much longer.