The short response is because they were the strongest of the three parties. After the conquest of Texcoco by Tezozomoc, in which the Mexica-Tenochca under the reign of Huitzilihuitl fought on the side of the Tepanecs, Tezozomoc gave some Texcocan land to the Mexica-Tenochca, therefore some of the Acolhua Texcocans were tributing to Tenochtitlan. Also, during this war Tezozomoc kills Ixtlixochitl Ometochtli and his son Cihuacuecuenotzi, rulers of Texcoco. However, Tezozomoc did not kill all the Texcocan nobility for Nezahualcoyotl survived and took refuge in Huejotzinco, a community in the Puebla Tlaxcala valley.

After Tezozomoc died, there was a bit of conflict among the Tepanec elite because they were fighting for the throne of Azcapotzalco. Tezozomoc had designated as his successor his son Quetzalayatzin from Tlacopan/Tacuba. However, the Tepanec Imperial council opposed the election of Quetzalayatzin and instead appointed his half brother Maxtlatl from Coyoacan. This broke the rules of succession and open up the possibility for a civil war among the Tepanecs. At this point, Maxtla ordered the assassination of his nephew Chimalpopoca, ruler of the Mexica-Tenochca and son of Huitzilihuitl, for supporting Quetzalayatzin in the succession process. Bare in mind that Chimalpopoca was in the unique situation of being half-Tenochca half-Tepanec, contrary to the rest of the Tenochca nobility that were Half-Tenochca half-Culhua. So after the dead of Tezozomoc, Chimalpopoca was basically left without supporters. At this point the sources are a little vague since some say that Maxtla killed Chimalpopoca, while others said that it was the Tenochca nobility that was half-culhua half-tenochca who killed him.

Regardless of who killed him, for the Mexica-Tenochca the dead of Chimalpopoca represented a break with the dynastic bond with the Tepanecs. At this point, the Tenochcas decided to elect a son of the first tlatoani Acamapichtli, to return to the royal line of Culhuacan. Itzcoatl was then elected as new Tlatoani. By his side he had as Cihuacoatl the great politicial Tlacaelel; combined they were able to obtain the promise that if Tenochtitlan waged war against the Tepanec, no other confederation would assist Azcapotzalco. At this point, Nezahualcoyotl returned from his exile, was crowned as tlatoani of Texcoco, and sided with his uncle Itzcoatl because he had a personal vendetta against the Tepanec Empire. Itzcoatl and Tlacaelel also managed to attract the assistance of the Tepanec ruler from Tlacopan/Tacuba who were not happy with the election of Maxtla against the wishes of Tezozomoc. So combined, the Tenochcas lead the attack against Atzcapotzalco with the help of The Texcocans and Tlacopans.