I considered myself centre-left in the 90s and centre-right now. And essentially believe the same things. Protect the country, the capitalist system, and those left behind by it. The latter was the main concern most of my life, as the other 2 were largely givens, but that's shifted in the last decade or so, thus the approximate shift in alignment, although it's always in limbo to some extent.
I think the primary downside of the right is nationalism and lack of compassion or awareness for those not suited by the capitalist system. I like the right when compassion and diplomacy are at the forefront, because their natural inclination for protecting the country and system is a given.
I think the primary downside of the left is a victim/martyr mentality that permiates almost everything, and it seems to be rooted in Marxist philosophy, which is particularly dangerous. I like the left when protection of the country and capitalist system is at the forefront, because the social safety net is always safe with them.
So I like both when they drift towards the centre, which generally means more benign approaches based in love and less vitriol. I dislike both when they drift towards the extremes and start hating everything about the other, which unfortunately is becoming more common.