Not all students can learn grammar. Research shows that some people have a more analytical learning style than others. Such learners are accurate but halting users of the target language. This observation by itself does not address whether or not all students can learn grammar. While it may be true that learners approach language learning differently, there has been no research to show that some students are incapable of learning grammar.
Students have different strengths and weaknesses.
It is clear that all students can learn grammar as is evident from their mastery of their first language. As grammar is no different from anything else, it is likely that students will learn at different rates. Grammar structures are learned one at a time. This myth is demonstrably untrue. Teachers may teach one grammar structure at a time, and students may focus on one at a time, but students do not master one at a time before going on to learn another.