Arjuna received basic as well as advanced lessons of archery from Kripacharya. Upto the level of four advanced methods of archery. Pandu being an exceptional archer obviously would've taught him earlier.
He then taught Kripa the four branches of the science of arms, and various other branches of knowledge, including all their mysteries and recondite details. In a short time Kripa became an eminent professor of the science (of arms). And the hundred sons of Dhritarashtra, and the Pandavas along with the Yadavas, and the Vrishnis, and many other princes from various lands, began to receive lessons from him in that science.'"
Drona’s school focused on specialisations and advanced techniques like Vyuh knowledge, fighting with multiple persons and so on.
Arjun became a seasoned veteran warrior under Drona's guidance. His excellence as well as years worth of training is evident from the following verses.
'Thereafter Drona began to teach Arjuna the art of fighting on horse-back, on the back of elephants, on car, and on the ground. And the mighty Drona also instructed Arjuna in fighting with the mace, the sword, the lance, the spear, and the dart. And he also instructed him in using many weapons and fighting with many men at the same time.
And hearing reports of his skill, kings and princes, desirous of learning the science of arms, flocked to Drona by thousands. Amongst those that came there, O monarch, was a prince named Ekalavya, who was the son of Hiranyadhanus, king of the Nishadas (the lowest of the mixed orders).
Arjuna's skills enhanced his fame throughout the land and hearing about it princes from other lands came to Drona's schools to be as skilled as Arjun himself.. One amongst those was the Tribal prince named Ekalavya. But Drona rejected him due to some reasons..
So he left and created a statue of Drona and began practising archery by himself Without any aid or guidance. Let us look at Ekalavya’s skill at this point of time.
The Nishada prince, touching Drona's feet with bent head, wended his way into the forest, and there he made a clay-image of Drona, and began to worship it respectfully, as if it was his real preceptor, and practised weapons before it with the most rigid regularity. In consequence of his exceptional reverence for his preceptor and his devotion to his purpose, all the three processes of fixing arrows on the bowstring, aiming, and letting off became very easy for him.
It's said that due to his determination, fixing arrows, aiming and releasing became so easy for him. These are the very basics of archery and he wasn't even proficient in those.
The starting gap between Arjuna and Ekalavya is Humongous. Arjuna has years of training and experience, proficient in 4 types of archery, possessed all celestial weapons barring Brahamstra and a seasoned warrior skilled in fighting with multiple warriors and in multiple weapons too, a veteran warrior. On the other hand, Ekalavya wasn't even a noob archer at this point.
Few months or years later…
Pandas went for hunting with their Dog and it strayed and encountered the tribal prince there. Upon seeing his filthy form, it began to bark loud at him. Just by tracking it's sound(sonic archery aka sabda ved), Ekalavya sent 7 arrows to its mouth sealing it shut without killing the dog.
It dashed back to pandas and upon seeing the handicraft of the marksman who did it pandas including Arjuna were amazed as well as ashamed realising their inability to perform such a feat.
The dog, thus pierced with seven arrows, came back to the Pandavas. Those heroes, who beheld that sight, were filled with wonder, and, ashamed of their own skill, began to praise the lightness of hand and precision of aim by auricular precision (exhibited by the unknown archer).
They met him and got the details and went back to Drona's school. Arjun however became incredibly jealous of him and saw Drona in Private.
He said ekalavya was far superior to himself and began to cry about it remembering Drona's promise to him that Arjuan woudl be his best student..
'The Pandavas then, having made themselves acquainted with everything connected with him, returned (to the city), and going unto Drona, told him of that wonderful feat of archery which they had witnessed in the woods. Arjuna, in particular, thinking all the while, O king, Ekalavya, saw Drona in private and relying upon his preceptor's affection for him, said, 'Thou hadst lovingly told me, clasping me, to thy bosom, that no pupil of thine should be equal to me. Why then is there a pupil of thine, the mighty son of the Nishada king, superior to me?"
Drona saw no other option but to permanently impair his skills, and therefore asked his thumb.
'On hearing these words, Drona reflected for a moment, and resolving upon the course of action he should follow, took Arjuna with him and went unto the Nishada prince. And he beheld Ekalavya with body besmeared with filth, matted locks (on head), clad in rags, bearing a bow in hand and ceaselessly shooting arrows therefrom.
And when Ekalavya saw Drona approaching towards him, he went a few steps forward, and touched his feet and prostrated himself on the ground. And the son of the Nishada king worshipping Drona, duly represented himself as his pupil, and clasping his hands in reverence stood before him (awaiting his commands). Then Drona, O king, addressed Ekalavya, saying, 'If, O hero, thou art really my pupil, give me then my fees.' On hearing these words, Ekalavya was very much gratified, and said in reply, 'O illustrious preceptor, what shall I give? Command me; for there is nothing, O foremost of all persons conversant with the Vedas, that I may not give unto my preceptor.' Drona answered, 'O Ekalavya, if thou art really intent on making me a gift, I should like then to have the thumb of thy right hand.'
The reason for Arjuna's jealousy and Drona seeking the thumb are exactly the same, Arjuna was no match to Ekalavya.
And the gap was not even close. A professional warrior was easily outclassed by a tribal nobody in a matter of few months or years. Such tremendous rate of growth as an archer made him a huge threat to Arjuna's stature.. Had he continued to improve Arjuna woudl've been left in the dust. Arjuna knew it. So did Drona. Therefore Arjuan was happy on seeing Ekalavya deprived of thumb and his jealousy left him knowing that without a thumb he would never be as good as himself.
'Hearing these cruel words of Drona, who had asked of him his thumb as tuition-fee, Ekalavya, ever devoted to truth and desirous also of keeping his promise, with a cheerful face and an unafflicted heart cut off without ado his thumb, and gave it unto Drona.
After this, when the Nishada prince began once more to shoot with the help of his remaining fingers, he found, O king, that he had lost his former lightness of hand. And at this Arjuna became happy, the fever (of jealousy) having left him.
Arjuna cannot surpass or even come close to Ekalavya no matter the amount of practise he undergoes or advanced techniques he learnt, Ekalavya was simply built different. If the case were otherwise Arjuna woudl've focused on improving his skills instead of whining to Drona. And Drona would've focused on training him harder instead of asking for Ekalavya's thumb. The fact is clear from the text..