During his duel with Anthony on Bridgerton, Simon decided to throw away his shot — even though that potentially meant being killed. Season 1 of Netflix's period drama revolved mainly on the eldest Bridgerton daughter, Daphne, who officially debuted during the London season. She ultimately ended up with the newly-crowned Duke of Hastings after the death of his father, but their romance wasn't a walk in the park; at one point, Daphne's older brother and Viscount Bridgerton was against their relationship, which led to his duel with Simon.
Anthony had every reason to oppose her sister's dalliance with Simon on Bridgerton; he had been friends with Bassett for a long time, and therefore, he's well-aware of his thoughts on marriage and relationships in general due to his experiences in his own family. But much like his insistence on matching up Daphne to the appalling Nigel Berbrooke, Viscount Bridgerton's objections didn't matter, unaware that it was merely an arrangement between his sister and best friend. In an unexpected turn of events, however, Daphne and Simon married in the hopes that a scandal about their secret encounter in the garden wouldn't reach Lady Whistledown and cause major havoc. Aside from Cressida, who was Daphne's rival for Prince Friederich's affections, they were also caught by Anthony. He immediately ordered the pair to tie the knot, but Simon refused, opting for a potential bloody duel instead of entertaining the idea of tying the knot, despite their obvious attraction to one another.
So, the long-time friends found themselves participating in a duel that neither of them really wanted to be in. Had it not been for Daphne's meddling, Anthony could've killed Simon after the latter opted to give up his shot, aiming upwards instead and giving his rival a clear advantage. Given this, why exactly did Simom even agree to the duel if he was planning to throw away his chance at winning it? The answer goes back to Simon's attraction to Daphne.
While Simon adamantly refused to marry Daphne, it didn't mean that he didn't feel guilty for what he'd done — and it certainly didn't mean he didn't want to be her husband. Allowing his emotions to get the best of him resulted in him committing actions that defiled Daphne's honor and put her in a precarious position socially. He made this abundantly clear during their wedding night when he came clean about the gnawing remorse in him for trapping her into a marriage that he thought she didn't want. Of course, he had assumed wrong and fortunately the pair cleared the air then and there. Thus, in his mind, dying in the duel would be his punishment for what he did, and Anthony being his opponent made it all the more fitting. In any case, he wasn't willing to kill his friend anyway.
Further backing Simon's decision was his low regard for his own value. Before Daphne, he didn't really have a purpose in life. He didn't take his role as Duke of Hastings seriously, in part because of the tumultuous relationship with his father. He was so steeped in his hate towards him that even until after he married Daphne and learned of her most fervent wish to become a mother, Simon was adamant that the Hastings line would not continue past him. As his wife put it, he was willing to give up the life and happiness that they could have together just so he can achieve his revenge on a dead man. Simon's stubborn commitment to this non-sensical promise meant that it was easier for him to accept the idea of getting killed in the duel with Anthony than to live his life.
Fortunately, things turned up for the Duke of Hastings. After he married Daphne and finally let go of his revenge plot against his father, life looked positively happy for him. At the end of Bridgerton season 1, he and his wife welcomed their son, whom he's more than happy to have in his life.