So let's go over fallacies here.
JARGON is real for each field.
It is taught that way.
The meanings vary by where they are taught. Even those taught the technical meanings you received don't use them in regular contexts.
There are plenty of other of regional differences in language (eg, UK & US English) not due to education: they're just different. Claiming differences such as this are due to lack of education is appeal to snobbery. The community decides the language as observed from their unsolicited usage in reports & communications.
Rightwingers are profoundly uneducated
While that may be so, that doesn't apply to the meanings of words the language community agrees on. Both the left & right in the US use liberals in regular contexts to refer to leftists who also refer to themselves that way. Telling an educated person in the US but liberals aren't leftists/progressives is liable to elicit an incredulous look like they're wondering if you're stoned or just stupid.
we can just use the words as they are supposed to be used and philosophically defined and others will pick it up or not
It's tendentious & misleading, because the exclusionary distinction isn't even correct, which leads to the next fallacy: false dilemma.
It's often claimed here that leftism & liberalism are mutually exclusive: no one can be both. However, by the technical definition they can be both, and by the North American meaning liberals are leftists.
North Americans treat the pursuit of values like equality & egalitarianism (individual freedom from oppressive inequality maintained by unjust policies) as related to the pursuit for individual freedom, so they identify them all with the words liberal & progressive interchangeably. This isn't an accident: the classic liberalism & enlightenment era political philosophy that founded the government were the progressive values of its time in contrast to traditionalist & royalist values. That association persists as the progressive cause continues to promote freedoms & a society with better access to opportunities & protections.
It's unsurprising the predominant variety of leftism there will include the pursuit of personal freedoms, ie, liberalism. These aren't incompatible or a sign of ignorance.
The line between liberalism and leftism is the support and perpetuation of capitalism, slavery, and authoritarianism
That is your bunk assumption based on fallacy. Logically, equality, egalitarianism, & personal freedom can all be pursued, which is both leftist & liberal.