Parallel test are dangerous when you don't think of state of system while executing test .
You are testing the same system in parallel,so one test can affect other test
For example , you have one suite that test delete user feature and suite that test create user feature.
In delete user , you deletes all users and validates the user list to be empty.
This works fine when no parallel tests are there , but when you run these suites in parallel , the tests may start to fail because by the time you try to check that user list is empty , the user creation test running in parallel might have created some users and your delete all users test fails
So run parallel tests only for test that are completely independent and are not affected by state of the system under test