Your description actually illustrates how terribly inaccurate the metaphor was. If enslaved people imitated the people who enslaved them, they'd be sitting in a rocking chair on a porch sipping lemonade.
The US has a unique and relatively recent relationship with chattel slavery so people are more sensitive to it now.
The earliest record of the master/slave terminology being used in engineering is 1904 by which point slavery was already outlawed in almost every country, including the US. You're right to say that chattel slavery in the US was a uniquely grotesque form of slavery, but there is no system of slavery in history where slaves are primarily imitating their masters. No matter what anyone's sensitivity to the topic is, it's a bad fit for what's being described.
If you ever try to tell someone the publicly released undisputed facts of the Iran-Contra affair, you will come across like a conspiracy nut because what happened is so utterly absurdly criminal and yet there were virtually no consequences for anyone involved. One fall guy went to jail for a while and then came out as a Fox News correspondent.
"The famously conservative president of the United States illegally sold weapons to a radical Islamist terrorist organization in Iran (the US's mortal enemy in the middle east) and then used the proceeds to fund Central American guerrilla fighters that were also narcoterrorists? And nothing much ever came of it? Hah, as if!"