A man resolved to move forward, and a woman determined to hide away, fall in love; unfortunately, the persecution he faces, and the scars she bears, threaten their future together.

It seems you’ve posted multiple loglines and most of them share similar problems.?I suggest reading through the formula tab at the top of the page, and the feedback other members receive to better understand the elements and format of a logline.

Both of the versions posted here share the same problems. They don’t have the elements a logline needs to contain aside from the protagonist.

For: “A man resolved to move forward, and a woman determined to hide away, fall in love; unfortunately, the persecution he faces, and the scars she bears, threaten their future together.” (30 words)

This logline is too vague. What persecution? Simply adding an adjective of whatever trait he’s persecuted for should fix that.
Specify the protagonist. Is the man, or the woman, or both?
What’s the inciting incident? It seems like it could be that they fall in love.
What goal does the protagonist pursue? Think of the climax of the story. What will have been accomplished at that point?

“A military veteran returns home after his father passes away, taking over his lawn care business and tackling racism, while dealing with his own grief and forming a tentative romance with a woman who has escaped an abusive relationship and seeks surgery to fix the scars on her damaged body.” (50 words)

This version suffers from the same problems, aside from the fact that it clearly specifies the man as the protagonist. It is also too long. Shoot for a version under 30 words.