I couldn't think how to word the title without writing my whole question, I am a native English speaker so while I understand saying "my legs aches" is wrong and sounds weird, I have no idea why. Same as saying "my back ache" is also weird.
"Leg" without an -s is the singular while "legs" with an -s is the plural.
"Ache" without an -s expects plural agreement while "aches" with an -s expects singular agreement.
Why do the singular (and respectively, plural) forms not agree in terms of '-s' or 'no -s'?