A single parity bit will not be able to spot all errors. Things will be fine as long as there are always a odd number of bits with errors in the packet. If there is an even number then the error will not be detected.

This example has only one bit in error. As we have an odd number of ones the destination can easily work out that there was an error. Because only an odd number of bits changed we can spot the error.

Here two bits are in error. The destination will not be able to work out that an error has occurred due to the fact that it sees an odd number of ones. As such this packet would have been accepted. As there is an even number of error bits the destination could not pick up the error.