Is it only possible to pay attention to one thing at a time?

Your speaker (not "teacher") is incorrect.

What the speaker (not "teacher") said was unnecessary non-sense and unrelated to Buddhism (which is about ending the causes of suffering).

For the speaker (not "teacher") to be correct, the speaker (not "teacher") must 1st define what an object or "thing" is. Since potential "objects" become infinitesimally smaller, it is impossible to define what a single object is.

For example, to perceive a "long breath" or "agitated long breath" or "smooth long breath moving from nose thru chest to abdomen" includes many different yet collective perceptions. It is impossible to perceive each of the above aspects of these perceptions individually.

For example, how can "agitated" or "smooth" be perceived independently from "breath"?

For example, to perceive a picture of a flower on a green wall can be done with one ordinary act of eye consciousness. To believe the mind is shifting extremely fast between objects of "picture", "flower", "green" and "wall" is superstition (maybe a worse more primitive superstition than reincarnation).

The Lord Buddha, who knows & sees, defined "perception" as follows:

And why do you call it 'perception'? Because it perceives, thus it is called 'perception.' What does it perceive? It perceives blue, it perceives yellow, it perceives red, it perceives white. Because it perceives, it is called perception.

SN 22.79

If the mind only could pay attention to one thing at one time then there would be no "contrast" (perception of difference) between different colours because the mind could only perceive one colour at one time.

For example, if the mind could only perceive one thing at one time then reading this forum would be impossible because the mind could not perceive the difference between the black colored letters and white colored background. The mind could not perceive the "vertical" line of the letter "T" and the horizontal line of the letter "T". The letter "T" could not be perceived.

The more one attempts to analyse this question (as I am attempting to do), the more speculative, theoretical and insane it becomes. Sheer madness & insanity. Utter adhamma.

The Lord Buddha, who knows & sees, described the vipassana required for complete enlightenment and the ending of the asava (defilements) as follows:

There is the case where a monk remains focused on arising & falling away with reference to the five clinging-aggregates: 'Such is form, such its origination, such its passing away. Such is feeling, such its origination, such its passing away. Such is perception, such its origination, such its passing away. Such are fabrications, such their origination, such their passing away. Such is consciousness, such its origination, such its disappearance.' This is the development of concentration that, when developed & pursued, leads to the ending of the effluents.

AN 4.41

If the mind could only be aware of one "thing" at one time then it could not perceive "arising" and "passing" of "aggregate". Without a sense of continuity, there would not be a contrast between "arising" and "passing". For "passing" to give rise to the disenchantment of "dispassion", there must remain some recollection or memory of the prior perceived "arising".

As mindfulness and concentration deepens that fact will gradually become more apparent.

As mindfulness and concentration deepens, superstition & deliberate false speech about things not truly experienced will be abandoned.

Thus the Buddha taught:

Discernment & consciousness are conjoined, friend, not disjoined. It's not possible, having separated them one from the other, to delineate the difference between them. For what one discerns, that one cognizes. What one cognizes, that one discerns. Therefore these qualities are conjoined, not disjoined, and it is not possible, having separated them one from another, to delineate the difference between them.

Feeling, perception, & consciousness are conjoined, friend, not disjoined. It is not possible, having separated them one from another, to delineate the difference among them. For what one feels, that one perceives. What one perceives, that one cognizes. Therefore these qualities are conjoined, not disjoined, and it is not possible, having separated them one from another, to delineate the difference among them.

MN 43

It's an excellent question.

In terms of eye optics there is a focal point where vision perceives whatever is in that focal point. But there often appears, with me, a complete flooding of sensory information where the whole picture is seen as one. It's as if the focal point has widened into the peripheral areas of vision.

This could be because saññā (perception) has ceased operating through the conditioned portion of mind. How so? When we perceive something, we break it down into sizeable chunks because that's how we were conditioned and it also seems more convenient. There's a car, a tree, a pigeon.

From both viewpoints, there is still only one thing being perceived. You can see a car, but you're also seeing the external components that make up that car. In the same way, you can see a busy city street in its entirety with all of the components that make up that busy city street. It's still one thing.

Your teacher is correct. It might be helpful to explore the Zen concept of the nen in regards to this topic. I find it a bit clearer than what I've heard from the Vipassana community (which isn't to say a clear, Vipassana explanation doesn't exist!). You can read about it here - the three nens.

The short of it is that the initial moment of perception - the first nen - always involves a single object be it eye consciousness, ear consciousness, etc. Each nen follows one after another like beads on a mala. Unfortunately, our mind left in an untrained state tends to see individual nens sort of smeared into each other. The calmer one's mind becomes, however, the more evident it becomes that only one first nen can be experienced in any given moment of consciousness. The second nen is essentially perception + reflection. Here, you would find Dhammadhatu's "long breath" or "agitated long breath" or "smooth long breath moving from nose thru chest to abdomen", etc. The third nen is discursive thought based on perception + reflection. Our example of the second nen mind object of "long breath" becomes "that breath was much longer than the last one!" in the third nen. It goes without saying that by the time you get to the third nen, you really aren't practicing anymore as you are waxing philosophic! ;-)

I.e:

Case 50 in the Hekiganroku, Ummon’s ‘Particle After Particle’s Samadhi’

Engo’s Introduction

Transcending all ranks, rising above all expedients; spirit corresponding to spirit, words answering words—unless he has undergone the great emancipation and attained the great use of it, how could he rank with the Buddhas and be a faultless exponent of the teachings? Now, tell me, who can be so direct and adaptable to all occasions, and have the free command of transcendent words? See the following.

Main Subject

A monk asked Ummon, “What is particle after particle’s samadhi?” Ummon said, “Rice in the bowl, water in the pail.”

Setcho’s Verse

Rice in the bowl, water in the pail! Even the most talkative can add nothing.

The North and the South stars do not change places, Heaven-touching waves arise on land.

If you doubt, if you hesitate, Though you are heir to millions—trouserless!

What does particle after particle samadhi look like? I'm pretty sure you've got an idea!

The teacher is correct.

It is only possible for the mind to hold a single object at a time. Thinking that the mind is able to hold multiple objects at the same time is merely an illusion of continuity. It is just the mind shifting very rapidly between objects and mindfulness is not yet strong enough to register/discern that.

As mindfulness, concentration and insight matures that fact will gradually become more apparent.

By practicing Vipassana meditation one can come to clearly experience this fact.