Bad woman. Evil. Harlot, slut, whore, cocktease. Villainess, assassin, murderer, sociopath. These were but a few of the descriptors that men seemed hell-bent on using to pigeonhole and define Natasha Romanova. She armed herself, building a wall of words used to wound to armor her soul. In this way, she would bleed and bruise, but never fall. For if you build armor with that which is meant to pierce, to strike, it shall never find its mark.
Men were marks, targets, husbands, or lovers. They were never friends or partners or to be trusted and relied upon. Barton changed that. He wormed his way into her heart, past her sharp words and carefully constructed barriers. He called her cunning, resourceful, and acknowledged her physical prowess without qualifications or excuses. Instead of whore, assassin, murderer, he called her agent. Instead of villain or monster, he called her partner. She was never bad, she was fearless. She was never call evil, but complimented on her calculated tactics.
So when Natasha told Loki she owed Barton a debt, she referred to more than just her life. She had survived and existed without Barton and could do so once again. But with Hawkeye covering her six she did more than survive. She thrived.