Your moon is in the 4th, which is a natural home, and does suggest a caring nature. However, it is in Sagittarius which is not an emotional sign, it's very much more philosophical and big picture.
The moon in the 4th in Sag might suggest someone with a foundation, and attitude to home, family and putting roots down that is very uncommitted, philosophical, and restless, moving to the next horizon.
This moon opposes Sun and Mercury in Gemini in the 10th, suggesting a highly mental and logical nature, which manifests in the area of public front or reputation. So not a personal or emotive house.
Maybe the opposition of these key personal planets in the polarity of Sag and Gemini just makes you very mental rather than emotional, and as these are angular houses they are more significantly felt.
As I say, the fact that the moon in the 4th is caring position, and yet is in a rather uncaring(personally speaking, as you are describing) sign, is possibly what emphasis this disconnect how that you experience your moon, your feeling nature. Your concerns would be much more mental and philosophical, and your attachment could be to travel and abstract ideas.
You have Chiron in the 4th in Sag(0 degrees significant) so this would suggest a wounding manifesting in your emotional life, which could manifest in a spiritual crisis, or a crisis of belief. You may feel a lack of wisdom or understanding relating to emotions, that something went wrong in this area. You may not listen to advice about your emotional life. You may also feel confined here. You may learn or giving the Chiron gift seeking for deeper answers and meaning through spirituality, philosophy or finding your own truth in terms of emotions. It does generally seem to suggest a very philosophical nature with emotions
You also have Saturn on the MC in Taurus. This is like a ultra selfish, possibly callous, ambition and money aspect, so although it is not a personal planet and house I'm addressing, it would definitely have an effect on overall temperament and self (and others)perception.
You have the North node in the 12th, which apparently is regarded as a loner aspect. It is also about learning to live from the heart more, and your SN in the 6th suggests analysis and criticism of the world around you, and as it's in Aquarius you may have a very impersonal and detached attitude in this. With Leo NN in the 12th, it would seem to be a about a more personally involved approach to the greater good-about more sacrifice to others, but maybe this is where you feel resentment or that you don't care or wish to care...?
From your chart, maybe it is that your emotional nature is better manifested in the larger picture, more spiritual, humanitarian or general causes, than on a personal level- maybe this is why you don't feel it in these areas of your live.
Yes the Leo NN is a personal sign, but that's the approach -the areas of life is the ultimate transpersonal.
And the significant angular, MC Saturn may suggest that a lot of your hard earnt satisfaction is from public endeavour and wealth.
This is before I got onto Pluto.
Overall the 3 planets in such an unemotional and mental sign in the house of your emotional nature would seem the biggest indicator to me.