Like did none of his advisors or military staff see how brain dead this move was? Why did Lopez even do it; surely no one can be that stupid.
It's not that simple as you are portraying it.
Paraguay had an alliance with the (Argentina) Federalists and the Uruguayan Blanco Party. Brazil had an alliance with Argentina's Unitarians and the Uruguayan Colorado Party.
Argentina and Uruguay were in constant Civil Wars.
The war started when the Colorados, with support of the Brazilian Empire, took power by overthrowing the Democratically elected Blanco Party. For that reason, Lopez declares war on Brazil, first taking a Brazilian ship in the Paraguay river, and later invading Corumbá.
After the rejection of Mitre, to allow Paraguay troops to go through Argentina, Lopez decided to open two fronts in Argentina, one to capture Corrientes and the other to go parallel on the Uruguay river to get to Uruguay somehow. Lopez expected that Urquiza, leader of the Federalists, to join an alliance as he promised, but later it was known that he was bought by Mitre and the Brazilians to stand by. Once Lopez's troops were on their way to Uruguay, the blanco party fell completely, and Paraguay was alone against all three.