Is taking an avocado pit from the avocado on Shabbos an Issur of Borrer?
No, this is not an issue of borer.
The pit of the avocado cannot by any means be considered a “taaroves” (mixture) with the avocado, so that there’s no problem of borer.
This can perhaps be distinguished from the issue of smaller pits, that can be considered as being “mixed” with the fruit.
Although some are stringent for this matter, and take the “fruit from the pit” rather than the pit from the fruit, it seems that one can be lenient here, certainly when this is done right before eating.
See Shemiras Shabbos 3:17.