GenX and Millenials both grew up with technology. The only real difference there is that when the internet, and later, smartphones came into popular usage most GenXers were already in their 20's.

I think this chunk right here identifies the flaw in your reasoning

GenX covers those born in the early-mid 60's(we'll say 63) to those born in the early 80s(we'll say 83). This means that when the iPhone launched in 2007 that GenXers were 24-44 years old. That's a big window and results in a lot of different opinions and technical aptitudes. To say that when "smartphones came into popular usage most GenXers were already in their late 20's" is demonstrably false, the vast majority would already have been well into their 30s by the time smartphones really took off(significantly changing the internet)

Turns out that big blobs of population tend not to be homogenous and may have different opinions and experience regarding a variety of issues. They may agree with one group on certain points but disagree on others, and they will often disagree even amongst themselves

Attempting to categorize why "Gen X doesn't like Gen Y" is a fools errand and will lead you to nothing but worthless anecdotes.