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Could be due to your credit profile and that is why the lender wants to see more money down. Remember they are using the lowest mid score to determine credit worthyness and your score is 586.
Could be a DTI issue. What are your ratios?
Or it could be just this lender.
Find out the details before you start shopping for another lender.
Take a look at the VA Lenders Handbook, to see if the lender is following VA guidelines, or their own.
Because VA loans can be for the full reasonable value of the property, no downpayment is required by VA except in the following circumstances:
If a veteran has less than full entitlement available, a lender may require a downpayment in order to make the veteran a loan that meets GNMA or other secondary market requirements. The “rule of thumb” for GNMA is that the VA guaranty, or a combination of VA guaranty plus downpayment and/or equity, must cover at least 25 percent of the loan.