Your terminology is not quite correct. Congress does not veto a veto, it overrides a veto. And the reason for doing so would be that the members of Congress are determined to have their way. If they can muster enough votes, they have the power to put through their legislation, with or without the approval of the President.
The veto.
VETO
Congress can pass a BILL over the President's veto making it a law.
If a US president vetoes a bill sent to him by the US Congress, the president may choose to veto the bill. In such a case, the bill is sent back to the congress. If the Congress can come up with a two thirds majority, then the bill must pass as law.
when two thirds of each House of Congress agree to do so
Congress can override the Presidents veto by a Supermajority Vote (2/3 of members)
A president's veto can be overridden by Congress with a 2/3 majority in the House. If it is a pocket veto though, the veto cannot be overridden.
This action is called an over-ride or over-riding of a veto.
Using the veto indicates that the President disagrees with Congress and that Congress was willing to pass a law they against the President's wishes.
Congressional Override
Yes
Overriding a veto