We are required to allocated US representatives based on Article 1, Section 2, Clause 3 of the US Constitution. After each 10 year census, Congress is required to create a law that sets the process of apportionment for the next decade.

Apportionment Act of 1911 set the representatives for that decade. This act was especially important because the territories of Arizona and New Mexico were soon to be states and we needed to plan for that. This act also raised the number of representatives in the house to 435.

Fun fact: this apportionment lasted until 1930 because we failed to pass an apportionment act after the 1920 census.

So to answer your question the motivation to pass this law is that we were required to do so.