Strength is quite desirable. How can one stop lawbreakers without it? Some are obsessed with the idea of strength, leading to the idea of splitting everyone into two catergories: strong and weak. The strong deserve to live, and the weak will naturally perish. However, that sort of thinking hurts others and hurts one's rational abilities. I believe strength comes from a resolve, and determination to see it through, not the power to beat someone within an inch of their life. What do you think?

Strength is a generalization that falls into three categories: physical strength, mental strength, and emotional strength. Having all of these is a vital part of having any sort of strength whatsoever. An unbalance can lead to a vulnerability, making you significantly more weak.

And yes, your resolve does measure your strength. The particular area you must be strong in is defined by where you are in the world and what the situation calls for. Generally, you'll deal with logical situations in most settings while in a lot of dangerous places on the street you'll need a mix of mental and physical strength. Emotional strength is essentially only useful on the internet, and is probably the easiest to have. Those who don't have it could be considered weak in a way, but this doesn't justify what people might do to exploit that weakness and it should not be held against the person in question.

My strength comes from all 3, though I lack the most in physical. Still, I'm stronger than most of the people in my house, and I think that's an accomplishment in itself.

Strength (uncountable) is a creature's ability to endure things.
A strength (countable) is an useful ability.

Strength would be your capability. Your measure of being able to affect the outside world and those in it. To get this, you need inspiration and motivation as well as determination. Apart from the well known definition of physical power, it can mean your resilience to unfortunate events. The latter was wonderfully described in the game Mother 3: 
"No one is simply born 'strong'. People only grow stronger little by little, by encountering difficult situations and learning not to run from them, no matter how frightening or daunting they may be."