Your observations are quite correct in a capitalist mould. Survival of the fittest and stepping on your neighbor due to ambition or desire to achieve something is quite common.
We cannot, quite simply, get out of that mould in a day or even in a week. This is due to the mental model we have created for ourselves and the world around us. We are quite literally aping the animals because their environment is a
survivalist mould and can only do so much for their species. Having said that, there are a few animals who are sensitive and capable of compassion and love. Dog is one such being you mentioned.
There is a human core or collective consciousness in us, that is empathetic and capable of kindness and compassion. This is by realizing the fact that we are all capable of feeling and emotions and need not hurt or lie to each other for perceived success. Of course, doing what you must, as a duty in daily life to achieve some goals is important, but definitely not at the cost of others.
I would go further and state that this consciousness need not be human alone. This includes all sentient beings, including animals and insects.
In metta meditation, we visualize the well being and happiness of every sentient being starting from our inward "happy" core and spread the vibrations of goodness to every living being on the planet including trees and plants.
In all this, it is important to recognize the ego (mental model of a "fixed, permanent being") in our reactions to any happening. For example, you creating a dent on my car in some way may hurt me mentally, even though it is only the car that has been damaged in some way. We don't recognize the fact that our mind, our body, our possessions, our relatives, are all ever-changing and impermanent. The solid core, that is the created ego, is capable of changing a man into a monster. He is perfectly capable of calmness in every situation. But he changes into a monster because his ego perceives something did not go as per his desire.
Betrayal is not the only scenario. It is part of the whole sphere of emotions that we are beset with in contemporary society. We are quite simply slaves to it.
How can we teach our friends Betraying is bad ?
If the mind of a person is more open or broad, it would take in the aspect of human consciousness among us all and work toward well being of oneself as well as honor good relationship with other beings. Simply recognizing the fact that we are all human and together on this earth, feeling the same things, positive and negative, should open up the person's "intrinsic goodness". Even better if it is toward animals and plants also.
AND most importantly How can we make our mind when someone Betrayed ON us ??
Any "perceived" attack on me is my ego telling me, "Hey! He/She hurt me! Look what he/she has done! Do something about it! Hurt them back!". The ego always acts in self-preservation. It is something that is a creation with no truth in it. And this is why we practice mindfulness and awareness, so that we can capture moments like this "perceived injustice" in our mind, recognize the ego, think clearly and work more constructively toward a solution rather than blindly reacting and worsening any situation.