You're the sexist is a silencing tactic sometimes used against complaints of sexism, which can be thought of as analogous to the "whoever smelt it, dealt it" tactic children use when disclaiming responsibility for having farted.
"Noticing gender is sexist!"
The assumption here is that the way to achieve a post-sexist society is to never be aware of gender and therefore sexism. Feminists generally argue the opposite about sexism: that open and intense criticism of sexism (raising awareness) is part of the process of achieving a reduction in sexist rhetoric.
The goals of most feminists are to eliminate discrimination based on gender, the inflexibility of current gender presentations, and the gender binary, not gender itself. It isn't necessarily a feminist goal to create a society where no one advertises their gender or where people's gender is generally unknown. When "eliminating" gender has been proposed by feminists, it has sometimes gone along with transphobic rhetoric complaining about how trans people reinforce binary notions of gender. Rhetoric about "eliminating gender" seen in wider culture usually also consists of little more than telling women to act more like men.
In any event, in present society, gender is so clearly signalled by many people as a key part of their identity (and when someone's gender presentation is ambiguous or non-binary they are aggressively discriminated against and attacked) that it's possible to be extremely sceptical of most claims of someone not being aware of gender as a category.
"You saw the sexism, that makes you the sexist"
In this argument, a person objects to a sexist action or text, and someone else says that the action or text had multiple interpretations, and that seeing the sexist one as primary means that the person complaining is more sexist than other people.
This appears to be an adoption of the implicit association results in some way: the argument is essentially that in order to stop being sexist, one must empty one's mind of sexism and therefore make sexism an alien discourse to one's mind. Therefore, seeing sexism is a sign of being incompletely anti-sexist.
However, feminists argue that it is simply impossible to stop being sexist by a force of will (many/most feminists are biased on implicit association tests), and that failure to actively criticise sexism simply allows the highly sexist status quo to continue. Therefore criticism of sexist messages (even if mixed or ambiguous) is a natural part of feminism, not a sign that one is actually more sexist than everyone else.
In addition, women as victims of sexism are more likely to actually notice it—people don't notice things that don't impact them personally as much. Therefore, this framing silences women: if they mention sexism, they are being sexist!
In general, being feminist doesn't require pretending that one doesn't know about or hasn't to some extent internalised society's sexism.
"Talking about sexism victimises women"
The argument is that by saying that a certain action was sexist, the person complaining must be saying that women are weak, vulnerable, humourless or otherwise different from and lesser than men, who are not affected by the action and must therefore be stronger. Thus, the person complaining must be a sexist.
In fact, sexism's impact on women is not due to their inherent vulnerability, it is due to their oppression by the patriarchy. So someone complaining about a sexist action is not belittling women, they are asking that women not be additionally oppressed. Stating that a woman is a member of an oppressed class and therefore a target of sexism and likely to be disproportionately affected by it is not an insult to that woman.
Note that it is possible to excessively attempt to protect women from sexism, see White Knighting.