Diana's breaking the boundary bonds of domestication and balances the battle of female equality is what makes her likable.
Through Wonder Woman's origins we are introduced to an alegory of a woman who was sent as an emissary with the understanding that she can change the outside world. She's raised as a royal princess with all the hierarchy raised to believe that her limitless abilities are equal to a man. But once she learns that compassion can bridge the gap of outside world, the love for that same world sets her apart in conflict to her culture's aspirations. Wonder Woman has denied her own heritage believing that she and her Amazonian sisters will one day live in harmonious peace.
Wonder Woman can get incredibly lonely.
In literature, Diana is a woman who doesn't fully understand how to love a man. Her naivety can hinder herself in any relationships making her vulnerable to broken hearts or rejection. She's never needed the love of a good man. Therefore that choice of remaining independently single could hinder her goals of first understanding the male species before uniting them in peaceful harmony.
Many superheros use violent weapons such as bladed boomerangs, power rings, heat vision, the most notable weapon that Wonder Woman uses is her enchanted lasso. The lasso is unique to Wonder Woman as she serves as a vessel of Truth when confronting adversaries. Truth defeats the lies of man's world. The lasso then serves as a symbol of connection to tether her taming ideals. Her gauntlet bands are also seen as defensive weapons to turn aside any offensive aggression made by man.
In the DC Comics story arc titled Infinite Crisis published in 2005, Wonder Woman is the first character tempted with disobeying the "thou shall not kill" commandment. In the battle she finds her friends succumbed to the powerful mind manipulator Maxwell Lord. Wonder Woman uses her lasso of truth to discover that the power that holds her best friend Superman captive. Lord's only claim that his death is the final resolution to free her mind-controlled friend. Wonder Woman's ultimate decision to take a life to save another results in her own selflessness potentially sacrificing her own immortal soul. Despite her good intentions, she is shunned by her superhero peers.
Everything that Wonder Woman stood for in the 1940's is now flipped in the opposite direction. Her belief that men and women can live in peace and harmony is not the same level as the post-modern feminist movement is. This only confuses her mission further by not only dispelling the masculine evils of misogyny, but she has to combat some of her own female gender who seek empirical power.
Wonder Woman is an ambassador for truth and harmony. It's all she can do.It's all she was raised to do.But for her alter-ego Princess Diana of Themyscira, she knows it's the measure of a woman to be free to achieve a woman's full potential.