Pfthb

The professor was visionary:

with the ability to imagine how a country, society, industry, etc. will develop in the future.

(Cambridge Dictionary)

In British English the word is far-sighted.

far-sighted adjective UK ​ /ˌfɑːˈsaɪ.tɪd/ US ​ /ˌfɑːrˈsaɪ.t̬ɪd/

far-sighted adjective (WISE) ​

uk having good judgment about what will
be needed in the future and making wise decisions based on this:

Buying those shares was a very far-sighted move - they must be worth
ten times their original value now.

https://dictionary.cambridge.org/dictionary/english/far-sighted

However I believe that farsighted in American English may have a different meaning.

EDIT

Based on discussion in the comments below and thanks to the link provided by Chappo, I quote Merriam-Webster. However I also note that Timbo would assume hyperopia by default. I defer to native speakers of AmE in their knowledge of their own version of English.

farsighted adjective far·​sight·​ed | ˈfär-ˌsī-təd Definition of
farsighted 1a : seeing or able to see to a great distance b : having
or showing foresight or good judgment : SAGACIOUS 2 : affected with
hyperopia

https://www.merriam-webster.com/dictionary/farsighted

You can say that the professor was ‘luminary’ - a shining light that inspired or guided others, or illuminated their path.

Definition: ‘a person who inspires or influences others, especially one prominent in a particular sphere.
"one of the luminaries of child psychiatry"
synonyms: leading light, guiding light, inspiration, role model, hero, heroine, leader, expert, master; More’

You can say the professor was far-seeing:

Having shrewd judgement and an ability to predict and plan for future eventualities.

This word is quite simple and yet has a connotation of acumen and shrewdness.

I went with:

Sage: ​

Wise, especially as a result of great experience.

Which can be used as noun or adjective.

"The professor was sage, and used that attribute to guide his students towards the right direction."

Alternatively:

"The professor was a sage, and guided his students in the right direction."

"See the big picture" is itself a little ambiguous.

If you're thinking of seeing how all the parts fit together at a given point in time, consider astute, perceptive, observant, or insightful:

astute (adj.) having or showing shrewdness and an ability to notice and understand things clearly

perceptive (adj.) characterized by sympathetic understanding or insight

observant (adj.) Keep, perceptive

insightful (adj.) exhibiting or characterized by the power or act of seeing into a situation

However, the student-teacher example makes me thing that you may be looking for an adjective that means the teacher can see how a situation may play out over time.

In that case, consider perspicacious, far-sighted, or even plain-old wise:

perspicacious (adj.) of acute mental vision or discernment

far-sighted (adj.) having or showing foresight or good judgment : SAGACIOUS

wise (adj.) characterized by wisdom : marked by deep understanding, keen discernment, and a capacity for sound judgment.

(All definitions are from Merriam-Webster online: https://www.merriam-webster.com/)

To approximate the ability to see the big picture in a single word, we can perhaps use clear-sighted.

The professor was clear-sighted and used that to guide his
students towards the right direction.

ODO:

clear-sighted ADJECTIVE

Thinking clearly and sensibly; perspicacious and discerning.

‘a clear-sighted sense of what is possible and appropriate’

‘What is needed is a clear-sighted reappraisal of where we stand,
before we can plot a path forwards.’

perspicacious ADJECTIVE

Having a ready insight into and understanding of things.

‘If only our parents could have been perspicacious enough to see our
talent and force us into showbiz.’

discerning ADJECTIVE

Having or showing good judgement.

‘Physicians are by inclination and training discerning men, wise in
human relations and keen in judgement.’

Lofty, or Sublime. Expansive is close, with a strongly benevolent meaning. Something along those lines, lot's on this page here... --> https://en.oxforddictionaries.com/thesaurus/lofty

I can't think of a single adjective, but "The professor didn't lose the forest in the trees" could be a useful idiom.