Privilege is a word loaded with connotations about being born with a silver spoon in your mouth.
White privilege isn't about being upper class because you're white. It's about the advantages a white person has over non-white people of the same station.
A white person in a poor neighborhood is on the whole more likely to be able to pull "themselves" out of poverty, because, the systems and power structures in place have white people in power, or have systems that are fair on their face, but still lead to higher white hire rates or social mobility.
Nobody is disputing that some white people have it bad, they're simply pointing out that all else about your social status being equal, being white provides tremendous advantage over being non-white.
Also, it is extremely frustrating that people quickly start to include race when the discussion is about gender. As I said racial inequality is an entirely different thing from gender inequality. Police shoots black people more, white people get paid more. There, white privilege! But, Police shoots men more, men get paid more. Who is privileged? See the difference? Most of the problems black people face are also problems men face more than women, so you can't talk about those two as if they were the same.
s/white/male/g and the point largely still stands with mildly adjusted examples.
I'd argue overall it is on the whole easier to be a man in society than a woman for similar reasons (i.e. men have been in charge of power structures for longer and entrenched assumptions abound).
I hadn't thought about the perspective that men are more often killed by police than by women, and probably for similar reasons (i.e. subconsciously viewing men as more dangerous than women), but by and large as a man I don't fear getting shot by police on a traffic stop.
It could definitely be harder to break into a traditionally female field, as an example, though for sure.
Overall I feel the "male privilege" would be more pronounced than any "female privilege", though.
This is actually what intersectionality describes: we each have our own unique sets of advantages and disadvantages through the lenses of our race, gender, sexual orientation, etc.
In the vast majority of cases a straight white male is going to have the fewest disadvantages and most advantages in western society, because it's been designed for centuries around the straight white male as the power-wielder.