In part the reasons are perpetrated by media and culture. If you go back to the medieval period records men and women died at about the same rate and they both used predominantly drowning and hanging as method.

Think about the dramatization of suicide for a hot minute and poison shows up as having this stigma of being a woman's weapon or the "easy way out" more often than not the dramatic gut punch for men has been stuff like a gun to the head, hanging, jumping off a tall something... Something violent and effective and "brave" for lack of a better term. Certain types of death are coded as "emasculating" and those types of death are generally easier to rescue someone from because of the length of time between making the decision and actual death.

The deaths of women (at least provided they are not villians) in media are more often played up for gore and empathy when they are violently murdered but played down when it comes to suicide. Either the type used is quiet and gives the illusion of the peaceful end of quiet despair, it happens off screen or the camera angle changes to soften the impact. There is no comparative "unwomanly" way to die. This is in part because at some level it hits different. Executioners in women's prisons have reported that it effected them way more and caused mental traumas. People who make fiction use this to manipulate the way you're supposed to feel.

At some level with enough iteration you create expectations of what suicides are supposed to look like based on their individual thematic meanings... Which are coded by gender.