I would argue that most people are not bad at math - they simply struggle to understand math on the same time frame as the test schedule. This may be due to inattention by the student, failure to actively engage in the class and the homework, failure of the teacher to explain the material adequately or an underlying learning disability.
The good news is, much of this can be addressed - learning disabilities can be diagnosed by a competent psychiatrist, students can learn better study and learning skills, teachers can re-explain material in a different way, a tutor can be hired, etc. The important part is to recognize that struggling to learn math doesn't mean a student is stupid or "bad at math" - it means he/she is struggling and should seek additional help.
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A lot of people are bad at math because they aren't willing to study
Pick a math major.
Given these two characteristics, there are four possibilities: Some people are good at math and have bad writing skills. Some people are good at math and have good writing skills. Some people are bad at math and have good writing skills. Some people are bad at math and have bad writing skills. Leaving aside what it means to be "good" or "bad" at these disciplines, it is likely that these groups of people have varying amounts of genetic predisposition for success at these aptitudes and their environments provided varying amounts of support or resistance to help them fulfill their levels of achievement. If you're suggesting a causal relationship, that to be "good" at one necessarily implies being "bad" at another, I don't think such generalizations are useful.
Math is: you get problems, you solve them. English is: you get a topic, and you write anything you want, as long as it pertains to the topic. They are obviously not the same thing, so you will have people who are bad at English, who just happen to be good at Math.
You can't be good a everything.