The way I see it - our self cherishing mind manifests various responses toward different situations and people. Cowardice is just one of the many complex facets of the self cherishing mind. And don't forget it can also disguise itself as something virtuous but really it is hiding something very 'sinister' deep inside ourselves.
For example, it can fool our minds into thinking that we are not cowards but simply giving the victory to others. So, we choose not to speak up. And we may not realise that it is really covering up our own cowardice. Sometimes we can't even really see what's our true motivation. Hence, I always find it a little suspicious when people tell me that their motivation is pure. How can one really know that for certain, absolutely sure?
There are so many layers and disguises that the self cherishing mind puts up to deceive us.
Personally, for many years I thought I was sincerely practising Dharma and that Dharma was my true goal in life. But when certain situations arose, I found myself finding excuses or reasons (quite naturally and even unconsciously) to do other things but Dharma. Of course, I was too cowardly to admit even to myself that I was more attached to my love for travelling and not sitting in one spot and meditating for days.
The things we fear are the very things we hide from - be it consciously or subconsciously. And we may not be aware about some of these deep seated fears until we are truly "tested". Ordinarily, we may never come across a situation to see through the different layers of ourselves to find the truth. And digging within does require a lot of persistent effort and conviction in wanting to know the truth about oneself.
I used to be very merciless in judging people who are cowards. Then I realised that I was an even bigger coward inside.
So, these days, instead of judging others or losing respect for others, I look at myself and what I have been doing. At the end of the day, humans are really not that different. We are all afraid to experience pain and suffering. And there is no way we will willingly want to endure any pain and suffering for someone else. Because we can't even do it for ourselves.
It is very easy to pass a judgement on others. But when you are placed in a shitty situation, you might react the same way or worse. You won't know until you have gone through it and came out shining.
Personally, I see that our only real motive for doing and saying everything that we do is deeply entrenched in the 8 worldly concerns. Hence, we will do anything we can to uphold our 8 worldly concerns, even it is at the cost of someone else. That is how profoundly self cherishing we are.