The American Anti-Slavery Society, like many in the North did not like the war with Mexico at all. The society and others felt that the only purpose for the war was to help slavery. They thought that the war would only help get more territory in which white people would be allowed to own slaves.
The society felt this because all of the land that might be taken from Mexico would, of course, be in the South. Since the South was where slavery existed, it was natural to fear that any land added to the southern part of the US would also have slavery.
For this reason, the Anti-Slavery Society believed that the war was meant only to extend slavery. Therefore, it strongly disapproved of the war.
Note that the suspicions of the Anti-slavery Society were well founded. There was indeed a push for the extension of slavery into the territories acquired in the war with Mexico, and the battle over the extension of slavery would provide the impetus for the American Civil War.
Lincoln (then a U.S. congressman) was an outspoken critic of the War with Mexico. A link is given to a speech of his on the topic.