Disclaimer: I don't own Naruto.
Being a dad means having more confidence in your kids than they have in themselves.
Gaara gave that now infamous speech because he knew his children would be something in their lives.
When Zen was nervous that he wasn't going to pass his graduation exam, Gaara didn't bother listening to his concerns. Zen graduated first in his class.
When Seiko was scared that people who ran the chunin exams would give her special treatment for being the Kazekage's daughter, Gaara didn't demand that the chunin examiners treated Seiko any differently than any other participant(because that's really asking for special treatment) he simply said that she wasn't that special. He didn't know if the slap from Neji was worth it. Seiko didn't get any special treatment since she passed but wasn't the best one there.
When Unmei was hesitant to visit her Great-Uncle Hiashi after she graduated second. Gaara knew she had nothing to worry. Great-Uncle Hiashi had been very well notified that he had to treat his grand nieces and nephews with the utmost respect back when Neji was heavily pregnant with Zen. He could act like a major dick to them he just couldn't go overboard and hurt them. Hiashi knew he was strong but he wasn't that strong.
Gaara knew his children were going to be great after all they were his children.