How to explain that relationship with someone worthy of respect is more than just a friendship?

Buddhism does not teach blind respect towards authority figures entrusted with responsibilities.

For example, in MN 95, before giving higher respect or veneration to a monk, a lay person is first instructed to ensure the mind of the monk is free from greed, hatred & delusion:

There is the case, Bharadvaja, where a monk lives in dependence on a certain village or town. Then a householder or householder's son goes to him and observes him with regard to three mental qualities — qualities based on greed, qualities based on aversion, qualities based on delusion....When, on observing that the monk is purified with regard to qualities based on delusion, he places conviction in him....

MN 95

Similarly, Iti 106 certainly says parents are like 'gods' to be venerated by their children; however this is when the parents have compassion & wisdom:

'Brahma,' bhikkhus, is a term for mother and father. 'Early devas' and 'early teachers' and 'those worthy of veneration' are terms for mother and father. For what reason? Because mother and father are very helpful to their children, they take care of them and bring them up and teach them about the world.

Mother and father are called "Brahma," "early teachers" And "worthy of veneration," Being compassionate towards Their family of children.

Iti 106

Thus, when DN 31 explains how relationships are to be conducted between parents & children; teachers & students; and monks & lay people, DN 31 does so referring to the performance of appropriate mutual duties & responsibilities.

In five ways, young householder, a child should minister to his parents as the East: (i) Having supported me I shall support them, (ii) I shall do their duties, (iii) I shall keep the family tradition, (iv) I shall make myself worthy of my inheritance, (v) furthermore I shall offer alms in honor of my departed relatives.

In five ways, young householder, the parents thus ministered to as the East by their children, show their compassion: (i) they restrain them from evil, (ii) they encourage them to do good, (iii) they train them for a profession, (iv) they arrange a suitable marriage, (v) at the proper time they hand over their inheritance to them. "In these five ways do children minister to their parents as the East and the parents show their compassion to their children. Thus is the East covered by them and made safe and secure.

In five ways, young householder, a pupil should minister to a teacher as the South: (i) by rising from the seat in salutation, (ii) by attending on him, (iii) by eagerness to learn, (iv) by personal service, (v) by respectful attention while receiving instructions.

In five ways, young householder, do teachers thus ministered to as the South by their pupils, show their compassion: (i) they train them in the best discipline, (ii) they see that they grasp their lessons well, (iii) they instruct them in the arts and sciences, (iv) they introduce them to their friends and associates, (v) they provide for their safety in every quarter. The teachers thus ministered to as the South by their pupils, show their compassion towards them in these five ways. Thus is the South covered by them and made safe and secure.

In five ways, young householder, should a householder minister to ascetics and brahmans as the Zenith: (i) by lovable deeds, (ii) by lovable words, (iii) by lovable thoughts, (iv) by keeping open house to them, (v) by supplying their material needs.

The ascetics and brahmans thus ministered to as the Zenith by a householder show their compassion towards him in six ways: (i) they restrain him from evil, (ii) they persuade him to do good, (iii) they love him with a kind heart, (iv) they make him hear what he has not heard, (v) they clarify what he has already heard, (vi) they point out the path to a heavenly state. In these six ways do ascetics and brahmans show their compassion towards a householder who ministers to them as the Zenith. Thus is the Zenith covered by him and made safe and secure."

DN 31

In other words, when a monk, teacher or parent is angry, immoral, negligent &/or has wrong view, Buddhism does not encourage us to view them a "true friends", let alone as "Venerables". In the Parable of the Log, the Buddha taught some monks are rotten to the core & will not reach Nibbana.

For those with doubts about what 'true friendship' is, DN 31 explains in detail the 16 characteristics of false friends & the 16 characteristics of true friends. In summary:

The friend who appropriates, the friend who renders lip-service, the friend that flatters, the friend who brings ruin, these four as enemies the wise behold, avoid them from afar as paths of peril.

The friend who is a helpmate, the friend in happiness and woe, the friend who gives good counsel, the friend who sympathises too — these four as friends the wise behold and cherish them devotedly as does a mother her own child.

DN 31

This is not how it works. You don't beg for respect, you don't demand it. When you deserve respect, it happens naturally.