What is your method for choosing which units to pair in FE4, 13, and 14?

[MisterIceTeaPeach]

In my first FE4 run I really cared for best possible skill inheritance to have an easier time with Gen. 2. 

In FE13 + 14 it's a mix of fitting relationships and good skill inheritance. Like two units of the same class never came together. 

[saisymbolic]

My process of choosing pairs: favoritism for certain characters, chemistry between parents, and stats in that order.

I choose my favorite characters and focus on unlocking their support options, which admittedly can take a long while. Luckily, I don't have that many characters I trip over myself about.

Next, I decide which pairings I enjoyed the most. This step takes the longest for certain characters. For example, Mozu takes me the longest to pair in Fates, especially in Revelations, when I'm stuck between deciding between Kaze, Saizou, Laslow, Ryoma or Xander. Then, there are some like Odin, who I pair exclusively with Elise - Kagero if playing Revelations - which leads me to my final point.

Stats. I simultaneously care and don't care about stats. If a pairing I enjoy produces a kid with a decent stat spread, that's good. If it doesn't, I make lemonade out of lemons. The Odin-Kagero example is perfect for this, because it's obvious that their child will be a hodge-podge of stats. But their chemistry together, in my opinon, overrides that, so I just rock a Dark Knight Ophelia and call it a day.

On hair color, the only time I care about it is when dealing with the Avatar's kids. I don't care if Hisame gets Hinoka's garish red hair - he's not my kid. But I'll be damned if my Caeldori walks around looking like a clown with tacky celery-colored hair because I chose the wrong hair color when making my Avatar. So, when it comes to that, I have to plan early on if my Avatar is going to marry a first gen parent or if I'll slap them with a Avatar-exclusive; the latter of which is usually the case.

[Landmaster]

They need to be close in age.

They can't be related.

For parents, they give a non-tragic hair color to the child (we can't be embarrassing the kiddos out here in them streets)~

I just like them as a pair~ They don't have to be the "most romantically compatible" Support-wise, some couples I just end up finding really cute, so I'll end up keeping them together~

[Eltosian Kadath]

I chose other here mostly due to the fact that both of these answers are a part of what I consider, and some of the games have other notable considerations as well. For FE4 I always consider who will inherit the kingdoms/duchies in the end. Making sure I get all (or none on the rare FE4 sub run) of the children is also a factor (I mostly bring this up for the one male Corrin run of fates I did, when I finally got around to thinking about pairing I realized that the standard dating pool in all of the fates game is perfectly gender balanced before factoring in Corrin, so the only way to get all of the children was to have Corrin marry one of the women only Corrin can marry, or marry one of the children...ew). FE4 I tend to optimize (with constraints) a bit for the fun of it, FE13 I mostly think about relationship and which supports I haven't seen yet, FE14 I tend to think a little more about optimizing children (although relationship and supports are still considered).

[Thinks Their Own Way]

With how broken kids are in Awakening, a lot of the time it's me just experimenting with various pairs; I do what ever I feel like doing. With Fates it's various: hair colour, supports, how many kids I want to have Dragon Veins, class and skills for the partner and child, and also Elise x Odin.