St. Thomas teaches that the the aim of morality is integrating the passions as one with the will, freeing our will from being subjected to enslaving passions, and aiming them to their proper objects, as determined by nature, in fitting amounts for the circumstances, by means of habits called virtues. Or, in summary, the goal of human morality is to free, rectify, and unify a man’s inner life, interpersonal and intrapersonal harmony, or, in the words of Dante, to crown a man a lord over all of himself.
The problem with these other kinds of moralities that reject “objective standards” is that they ignore that our passions and inclinations have an proper end as determined by nature. There is a dimension where culture and society determine how these passions are to be inclined in particular circumstances, such as how different cultures approach the sexual appetite and marriage differently, and so there is a dimension of morality that is in a sense arbitrary or relative. However, even though different cultures approach the details and specifics of sexuality differently, most of these views still work under the general understanding that the object of the sexual passions is perpetually one of the opposite sex, especially at the popular level. This is because the inclination cannot be fulfilled or even made sense of without appealing towards its object, as determined by human nature. This is where natural law and psychology help us grow in the self knowledge need to cultivate the virtues and uproot our vices. This is the seeds of the “objective standard” you are asking about.
When each inclination isn’t aimed towards its object, our soul is lost and unable to reach unfulfilled, left divided and in conflict with the other passions, reason, and will, enslaving them to the disordered passion. We are left like Christ on Good Friday, a mob (the passions) rebelling against their true king (reason).
And if our inner life is not in order, we usually are inclined to act in contradiction to God’s will. This is because the goal of morality, to interigate, straighten, and free our soul and will, is itself a means, towards integrating and aiming our purified soul towards God. This is what C. S. Lewis means when he says that the way to the Promised Land travels past Mt. Sinai, and what St. Thomas means when he says that morality is not the ultimate end of man, but rather beatitude, the Beatific Vision.
So, in summary, without the objective standard that nature provides, we cannot make sense as to the aim of our passions and desires, and end up indulging in them mindlessly and ordering them towards all kinds of arbitrarily chosen excesses, deficiencies, and perversions, leaving us conflicted enslaved within ourselves and with others, and unable to even approach even an earthly fulfillment, let alone our true fulfillment that is God. If our very life and being is in such a mess, we simply cannot love God with all our life and being, nor can be love our neighbor as we love ourselves, as our very heart is unable to love ourselves correctly, nor come together as one to act for the sake of God. Our strength is used in one way, our heart in another, our soul in yet another, and so on. No unity, just war between ourselves and our neighbor and our God.
Christi pax.