Obviously, an act that promised to end discrimination based on "race, color, religion, or national origin" posed a threat to the sensibilities of a man like Smith on like three or four different levels. So how could he throw a big ol' bigot-wrench in its gears? Simple: by adding one more, tiny word to that list: "sex." Not as in "everyone is entitled to equal amounts of it" but as in "women get equal rights too."
Now, as you can probably guess, Smith didn't give two shits and a ham sandwich about women's rights. This wasn't his way of squeezing one desirable outcome out of a bill that he saw as the downfall of his entire belief system -- it was his way of splitting the vote. He knew that there was a large contingent of members who were all for maintaining a dong-advantaged society, and adding women to the act was a way to make it sound so ridiculous that on-the-fence congressmen would Humpty Dumpty right down to the "no" side of the yard.
United States House of Representatives
If he really wanted division he should have just included something about pizza-topping preference.
When he introduced his smart-ass wording change, Smith was met with a wave of laughter from the House floor. But laughter can be misleading -- Smith either vastly underestimated the level of support behind the Civil Rights Act or completely failed to realize that somewhere around half of the population maybe, you know, wanted women to have equal rights too. The bill passed, and not only did Smith possibly help cement its passage, but a man who was vehemently opposed to granting blacks and minorities equal rights also accidentally helped jumpstart the modern feminist movement. Just think of how embarrassed he must have been when he realized that women also come in all colors.