Even for cancers that shouldn't be sex-specific, like lung cancer, men are less likely to survive it.
The physical rotation/tumbling of molecules in an MRI is also very important, because the strong magnetic field is the thing inducing the "up"-vs-"down" split in the first place, and if the molecular motion is happening at a certain frequency with respect to the external magnetic field there are other interactions that can come into play which can affect the coherence of the nuclear spins (i.e. they can fall out of sync). Thankfully, the rotation of a small molecule like pyruvate is very fast (might higher then the "spin" frequency-a.k.a the Larmor frequenct of 13C at the magnetic field strengths involved in MRI) so the physical tumbling of pyruvate doesn't really come into play when trying to measure its signal. It can be another story for molecules that don't tumble quickly, like the ones that make up tissues, fat, etc.
Worth reminding the women in your lives to check their family history and consider getting early exams either way. A lot of times it turns out women do have family history that went undiscussed until they ask mom, aunts, grandmothers, etc.
The other cancers that worry me are the slow moving imperceptible symptomless ones like pancreatic, liver, kidney, etc. Know a few people who around 50 discovered they had stage 2-3 cases due to unrelated scans they got from an accident injury. Some of these you have 5-10+ years window to treat it and live without impact to lifespan.. but most people don't catch it until stage 4 when they actually feel sick and it is too late.
Just went to a funeral this weekend for a 40 year old who died of breast cancer 4 weeks after diagnosis at her first annual mammogram.
A lot of skeptical people under 30 here haven't lived through regularly various cancer diagnoses in their friends & family group that your late 30s/early 40s starts to bring.
I don't have the data on it, but anecdotally I notice that women's cancers seem to strike 5-10 years earlier than mens even if they can be caught early & treated well.. Though apparently men have overall worse cancer survival rates.