For example, if you have a really unique display face full of personality, you'll need something more neutral to do the hard work and create a balance. It's important to balance personalities in font pairings too. Our mind ends up confused – is this a different font or not? Good contrast is often provided by pairing a serif font with a sans-serif font. For example, overly similar serifs or similar sans serifs don't tend to look nice next to each other.
If typefaces are too similar, it's likely that they'll conflict. Contrasting fonts can be hard to find as you're effectively searching for two fonts that are different but also complement each other rather than causing conflict.