I am relatively new to using ANOVA, I would be grateful if you could help answer my question.

I am performing a single factor ANOVA test for three groups, The test reveals statistically insignificant results for the three groups.
Then, just out of curiosity, I decided to perform the ANOVA for 2 of the 3 groups and I received statistically significant results. Is this possible? Why did this difference not show up in the test with all 3 groups?
If it had, I would have used Tukey test to perform a post-hoc analysis......

In short, what interpretation shall I make if I receive insignificant differences for 3 groups, but when I test 2 of those groups separately, the differences are significant?

Many thanks