How can I have clamydhia but my partner doesn't?

Usually both have it. Whether or not one person catches chlamydia from another depends on things like: which part of the body has it, which parts of the body are the people touching each other with, how often are the people in contact with one another, etc... Also, tests are not perfect, so sometimes a person has it but has a negative test result. Usually, both people take the antibiotics if one person has chlamydia.