You got some impressive word choices; however, you seem weak in finding the correct noun + preposition combinations. Cohesion and coherence are also lacking. Moreoever, relevant examples, despite being part of the requirements, are completely absent in your essay. All things considered, certainly you can land a 5 or 6 with this essay, but higher scores demand a better grasp on cohesion and coherence.
The detailed correction is as follows:
People have different views about on whether everyone deserves the right to learn in higher education no matter what their level of academic ability is. Personally, I must take issue with this statement as limited quantity of university admissions creates essential competition among students and enhances the quality of education.
→ For an introductory paragraph, it is essential to paraphrase the statement in question before stating your opinion because the statement is not a part of your essay. Try not to cut corners with a mere mention like this statement, or you'd get marked down for cohesion faults.
To commence begin with, the small number of university admission generates necessary competition. Obviously, each student is awares of merits as well as opportunities when he learns at university, namely practical experience and valuable relations. Thus, he must put more efforts into learning in order not to lose the chance of his lifetime into others’s hands. It is a competition that makes students concentrate their mind on learning. Only when students struggle to attain their targets can they treasure their results. If everyone takes studying at university in for granted, they sooner feel bored sooner or later with and cannot take advantage of university knowledge.
→ Commence and begin are similar in meaning, but you cannot use synonyms in set phrases like 'to begin with'.
→ Two underlined sentences should be rewritten into one.
Additionally, limitting the number of university students improves the quality of education. Firstly, not all the students indeed have reached the same academic standards, while university requires students to be skillful, creative, and active to address diverse subjects. That strongly suggests that only students having overcome University Entrance Examination are accepted to learn in higher education. The same level of ability not only helps lecturers teach more easily but also accelerates speed of teaching. Secondly, when learning in a small class, students can utilise assistance from lecturers and pay more attention to lessons.
→ Addtionally serves better as a sentence connector and not a paragraph starter.
→ Pay more attention to the balance in your paragraph because your first idea (Firstly...) got too much focus while the second idea (Secondly...) is poorly developed.
→ Academic standards (hard skills) and being skillful, creative, and active (soft skills) are two different criteria. You should make clear what exactly the university demands (hard skills? soft skills? both?) from their students. And how would the entrance exam assure that everyone got the same level of ability once they pass? Do you mean the minimum requirements to keep up with higher education?
In short, university education lays the solid foundations of for people’s career; therefore, it is merely suitable for those who are absorbed in learning and strive for their dreams.
→ It is strongly advised that you shouldn't write a one-sentence paragraph for your conclusion.
→ The conclusion also lacks coherence: university benefits people who want a career (first clause), but it only suits people who are interested in learning and strive for their dreams (second clause)? You can have academic, spiritual or career dreams, so the dreams part needs to be specified as well.