Since Pro did not elect to define "education" I will do so here.
is the process of facilitating learning, or the acquisition of knowledge, skills, values, morals, beliefs, and habits. 
Pro does not differentiate between different types of schooling, so I only have to argue that any form of government-approved education being compulsory is beneficial.
While compulsory has many known benefits, the actual implementation makes it near impossible to fulfill in developed countries. My framework is that if any country can achieve compulsory education, then it is by definition, not developed. And if a country is developed, it cannot afford compulsory education. In other words, the premise tries to fit two impossible ideas together, which is paradoxical.
I believe that Pro meant to say "developing" in place of "developed" in this paragraph, as he conflates the phrase "developed country" with third world countries, while the opposite is the case.
I also disagree with Pro's definition of compulsory education in the description.
Compulsory education refers to a period of education that is required of all people and is imposed by the government.
In implementation, this definition is not strictly correct. For instance, the state of Israel enforces compulsory military service for all citizens when they turn 18. However, the word compulsory doesn't mean that there are no exceptions. One can be exempted from compulsory for religious and psychological reasons, as well as by the Defense Minister's discretion, among other reasons.
Pro's main contentions against compulsory education are in short, as I see it:
1. Implementation is difficult/impossible in developing countries as they lack the infrastructure/resources/motivation to support it.
2. The benefits of compulsory education are not as high as you would expect (a few relevant statistics are cited.)
3. Other necessities should be worked towards first, such as access to clean water and basic health amenities.
4. Impoverished families lose access to help around the home or in basic labor such as farm chores, especially since "with homework projects, lesser time can be used to attend to the house condition" (presumably costing even more time without even the benefit of free food during the hours spent on said projects).
5. "cultural barriers and prejudices must be lifted until both girls and boys have a good chance in their future careers. "
6. Corrupt government means that any attempts at implementing government-funded education will fail.
The form of education need not be as expensive as the United States system, which is bloated by years of bureaucracy and corpulent with the excess of a well-established nation.
I find it hard to believe that no education is better than some education, so unless Pro provides some form of proof that this is the case, compulsory education is preferable to voluntary IMO.
This is not an argument against compulsory education, only one towards less expensive options.
Homework projects are definitely unnecessary. There are options, such as supporting said families with utilities or groceries (similar to Food Stamps programs in America)
A1: Cheaper Forms of Education
Pro implies that compulsory education in developing countries would necessarily take the form of the kind of public, general education in a formal setting that is common in the United States, etc. This is a false dichotomy to me as there are many possible permutations of how education could take place, even practices that don't exist today. I will posit a few that would likely serve better and cost less below:
Informal neighborhood education: This would consist of a few educated individuals in a community working to teach valuable skills such as reading, writing, and basic math, and the basics to a few trades preparing children for higher-paying job opportunities, rather than being limited to the same basic job that their parents are doing. This wouldn't need to be as highly regulated (and therefore expensive) as the US public education system is, which is grossly unsuited for an infrastructure-poor society. This system would ideally cost little more than teacher wages and building upkeep. This is a first step towards higher educations rates in the developing country. Counters points 1 & 2.
Homeschool: Many impoverished families would find it difficult to put substantial amounts of time towards directly educating their children and many would lack the requisite knowledge, as they never received an education themselves, if even a small amount of reading could be enforced in every home, it would improve the average literacy rates. This is a somewhat weaker option, but some form of homeschool should be on the table, especially in later years as children become old enough to teach themselves through books (which could be donated through charities). Counters 1 and 6, so long as some basic literacy and study ethics are instilled first.