Peacemaker has made it clear that he thinks very highly of his skills as a superhero since his debut in The Suicide Squad. His egotistical, and slightly delusional, perspectives press on in the Peacemaker series as he mocks various Justice League members for all manner ridiculous reasons. There is one Justice League member, however, that is spared the ridicule, but not necessarily for the most wholesome of reasons.
Throughout the past few episodes of the show, Peacemaker goes as far as to state that Superman has a "poop fetish" to his fellow teammates and tells a room full of elementary school students that the Flash is just a "douchebag." No man of the Justice League is safe from Peacemaker's snide comments, so what about Wonder Woman? Well, she obviously "eye f-ed" him from across the room at a party once as Peacemaker proudly goes on to tell the children during a show-and-tell. The titular hero definitely has some high expectations of himself.
Without a doubt, these comments are baseless and completely false, but Peacemaker's inherent misogynistic attitude and upbringing compel him to express himself in this way. Chris Smith is consistently questioning himself as a hero throughout Peacemaker and these offhand comments are an attempt to feel superior. Ever since he killed Rick Flag during the events of The Suicide Squad, Peacemaker has been losing confidence in his superhero identity and these consistent jabs at other heroes are clear signs of his growing insecurity. This is especially apparent when he mocks Batman for not killing his enemies while simultaneously doubting his own vicious tendencies.
Why else would he feel the need to tell a room of school children that he caught Wonder Woman starring at him inappropriately? This event definitely did not occur, hell even one of the kids says he sees right through him, but he stands by his statements because he is desperately trying to embody this macho-man, mercenary persona. Ultimately this pursuit of false "glory" through inappropriate and crude comments only further damages his superhero image rather than strengthens it. As the one elementary student states... he is kind of a loser for it. Making false and flagrant accusations against fellow heroes definitely doesn't seem like a very heroic move on Peacemaker's part.
During the most recent episode, however, Chris Smith does start to see some potential maturity as he further questions his methods as a vigilante. It is obvious the true Chris Smith, the true Peacemaker, isn't this heartless mercenary when he tells Harcourt he doesn't want to kill people anymore. His misogynist mindset and violent tendencies are traits he has internalized from being raised by the White Dragon, but Chris is beginning to slowly understand that this isn't the kind of person he actually wants to be. This is further reinforced when he stops himself from critiquing the "dove of peace" Harcourt draws on his gun. He accepts the gift while sharing a mutually respectful and tender moment with Harcourt that is void of childish and sexist comments.
These small moments are reflective of the fact that deep down Peacemaker is not this hypermasculine hero, but rather a flawed human with a hurt inner child and a naturally good heart. He is steadily beginning to transition from an unrelenting bro who tells people Aquaman had sex with a fish to being the admirable superhero he actually wants to be. Hopefully, by the end of the first season, Peacemaker makes his first big steps toward redemption and maturity because he really needs to stop telling school children that Wonder Woman tried to make sexual advances on him.