Are we not thinking of ourselves as either you're better than they are, or equal to them, or worse that they are?
From the Buddhist viewpoint, conceit is a delusion that convinces us that we are the sum of our experiences. When we compare ourselves to others, we create a sense of self in our minds. then that sense of self is involved in comparison to others that generates "self" inflicted suffering, which is where the concept of no-self comes into Buddhist thought as an antidote to that particular suffering.
According to the Buddha, there are three conceits. The first conceit, I am better that others, leads to pride and arrogance. The second, I am worse than others, leads to envy or resentment. The third, I am the same as others, generates complacency.
"And what are the three kinds of conceit that are to be abandoned? (1) Conceit, (2) the inferiority complex, and (3) arrogance: these are the three kinds of conceit that are to be abandoned." from AN 6.106, translated by Bhikkhu Bodhi
Conceit is among that which defiles the mind, and can generate several of the others on that list.
"Imperfections that defile the mind: (1) covetousness and unrighteous greed (2) ill will (3) anger (4) revenge (5) contempt (6) a domineering attitude (7) envy (8) avarice (9) deceit (10) fraud (11) obstinacy (12) presumption (13) conceit (mana) (14) arrogance (15) vanity (16) negligence" from MN7, translated by Bhikkhu Nanamoli and Bhikkhu Bodhi
Lastly, the short answer to your question is...Yes.
It is useful for thinking: "I can enter the path" but it is useless for actually entering the noble path because entering the noble path is based on abandoning the conceit "I am".
The four Best Kinds of Faith do not include the conceit "I can".
Faith, monks, also has a supporting condition, I say, it does not lack a supporting condition. And what is the supporting condition for faith? 'Suffering' should be the reply.
Now, any delight in feeling is clinging. From his clinging/sustenance as a requisite condition comes becoming. From becoming as a requisite condition comes birth [of 'self']. From birth as a requisite condition, then aging-&-death [of 'self'], sorrow, lamentation, pain, distress & despair come into play. Such is the origination of this entire mass of stress & suffering.
Now, there is the case where a Tathāgata appears in the world, worthy and rightly self-awakened. He teaches the Dhamma admirable in its beginning, admirable in its middle, admirable in its end. He proclaims the holy life both in its particulars and in its essence, entirely perfect, surpassingly pure.
He [the person discussed above], hearing the Dhamma, gains conviction in the Tathāgata and reflects: 'Household life is confining, a dusty path. Life gone forth is the open air. It isn't easy, living at home, to practice the holy life totally perfect, totally pure, a polished shell. What if I, having shaved off my hair & beard and putting on the ochre robe, were to go forth from the household life into homelessness?'
So after some time he abandons his mass of wealth, large or small; leaves his circle of relatives, large or small; shaves off his hair and beard, puts on the ochre robes, and goes forth from the household life into homelessness.