The idea was that the US entering the war by that point was inevitable and that it was clear that when the US joined it would be on the side of the Allies, Germany's idea was that if they could get Mexico to start another front in the war it would serve as a means to prevent the US from sending troops to Europe.

Now to answer your question specifically it is clear through Mexican-American history that tensions flared regarding certain territories as Texas was originally part of Mexico until it succeeded during the Mexican-American war. Therefore the reasons for war would have been the same as the France's aims of WW1 which consisted partially of regaining the lost territories in Northern France.

There were a lot of tensions between Mexico and USA back then, the American ambassador supported the overthrowing of the Mexican president in 1910, American forces occupied Veracruz in 1914 (300 mexicans died in that operation) and they sent troops chasing Villa without the approval of the Mexican government in 1917. Carranza also supported raids in Texas as a way to pressure them into recognizing his government. Mexico and USA were close to war several times between 1914 and 1917.