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It depends why you didn't get your surface warfare badge. If it was because you met all the criteria, but let's say were not recommended because of conduct, then your conduct and performance might only rate a general discharge, depending upon how you have been evaluated and the paper you were given.
Other than conduct, no, failure to achieve the badge in and of itself should not give you less than an honorable discharge.
Failing to qualify for a primary MOS, for example, murkiple time, could warrant a less than honorable discharge, as could misconduct.
If you were not required to obtain the badge, and received an lesser evaluation, that is not appropriate. Additionally, receiving less than an honorable would not be appropriate.
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