Only teaching children how to test well is obviously disastrous, but tests on skills like spelling, phonics and basic mathematics can help track a child's progress and uncover learning difficulties like dyslexia. There are also some subjects, thinking mainly within higher levels of education, where a sound knowledge of the subject matter is vital. Think of Biology, testing seems to be a pretty fair way to determine whether a student had learnt the information they need to know to get a GCSE, an A Level or a degree etc... This has further real life implications, I would not like to be treated by a doctor who failed their Biology A Level because it's a sound way of determining whether they have actually learnt the material vital for their profession.
In terms of self worth, students need to be reminded that test scores are not meant to rank them as 'less than' other pupils, but to help uncover the best way to help them learn as an individual.
Furthermore I don't believe that all subjects require testing, especially at Primary and Secondary levels of education. Subjects like history, art, RE and creative writing can be assessed in a less formal manner, though I think testing in any subject is fair should a student go on to pursue that subject at a higher level. For compulsory lessons (like history to young students) an interest and general understanding of historical events can be shown through class participation and independent classwork. They really don't need to be tested and scored on names and dates unless they decide to follow on with history after year nine.