Prompted by your comment, I re-read it.

• Arsenal. We all know the story, but it does go into detail.
• Despite playing well at Sheffield Utd, the rest of the team didn't. Relegated.
• At Newcastle he was competing for his place but both he and Nick Pope didn't perform well. Transferred.
• Southampton. Eckert doesn't rate him, but he is fighting for his place from a position of being 4th choice. Yes, it doesn't say why he is out of favour, but maybe it's not well-known?

Edit - I found the original interview and speed watched it. Begovic's quote in the article is:

"There's many different factors that go into it but I think it's been unfortunate that maybe a few things haven't aligned for him [at Southampton]."

The only factor he lists in the video are "club business elements".