I once saw this particular researcher who seems to like bragging about himself. So, I checked his profile on Google Scholar and he has around 30+ citations on one of his papers; however, I just found out half of his paper was cited by himself.

Is he in the right to be bragging about his accomplishment if his paper has been cited by himself?

No. That shows desperation.

Desperation?

Citing own stuff to get more citations and then bragging about it. He or she is desperate as others are not citing their work enough. This happens in normal course too, as you would naturally cite your own research in future work. But that constitutes half of your citation, it is far too high.

If he's bragging, that's pure arrogance.

However, if a researcher has been working on a given project for a long time with the same or similar methodologies then a researcher's later work will naturally cite earlier his work.

In searching for research validating their work, work of slightly differing methodology can be ignored or missed.

Ian (Mackem_Beefy)