I don't think it's anyone's business to tell others which achievements they are allowed to be proud of. However, in the interest of furthering this disussion with an even handed look at the stats, may I recommend the following links:
https://www.nuffieldfoundation.org/news/first-in-family-university-students-need-more-guidance-navigating-education-system
https://blog.ukdataservice.ac.uk/first-generation-university-students/
The Data Service analysis (2022) shows that a "first in the family" pupil is half as likely to attend university as the child of graduates. I think that that is still a massive gap, and that many of those students must surmount considerable obstacles in getting into - and, importantly, completing - university education. Here's an overview of their findings taken from the blog:
"Our research found that access to university is still not equal.
Take two young people of the same age, with similar GCSEs and who come from a similar socioeconomic background; except that one has graduate parents while the other has not. The one without graduate parents would be almost half as likely to go to university as the other.
More specifically, the probability of university participation by parental education is 34% for potential first in family students, while for those with graduate parents the probability is 72%.
While at university, first in family students are three percentage points less likely to attend elite universities than their peers with university-educated parents.
They were also four percentage points more likely to drop out of university than students whose parents have a degree, conditional on their prior attainment and a range of demographic characteristics.
We found that having non-graduate parents is one of the most important barriers to university participation; more important than free school meal eligibility and the neighbourhood where you live, for example.
Interestingly, among women, we found that parental education inequalities continue in the labour market.
In their mid-20s, first in family graduate women earn about 7% less than graduate women with graduate parents. Among graduate men, we find no such difference.
The female FiF-pay gap is partially explained through pre-university educational attainment and elite university attendance, working in smaller firms, working in jobs that do not require a degree and motherhood status."
As you can see, right through their tertiary education experience, these students have a harder time by dint of being "first in family" students.
The "first in family" effect is even worse for women, who it seems will continue to earn considerably less than equally qualified peers even after graduation.
So, I very much hope for the sake of any DDs that you may have that you do get a degree qualification. While the effect on earnings is not at an individual level, just the lousy gap on a cohort level makes it more likely that their earnings will be affected if you do not get a degree (unless their dad has one that is).
When I took my first degree (yes, as "first in family", Russell Group, 1990s) I was at a major socio-economic disadvantage to most of my fellow students (who were majority privately educated) - financially, aspitationally and social network wise. This makes a huge difference. About 20 years later I started another degree (with the aim of retraining), but had to drop out due to having a young family and the extra pressure of a child with ALN.
If you do indeed manage to complete a degree as "first in family" while also caring for your DC, you will be totally justified in feeling very proud of yourself. Don't let anyone tell you otherwise!