First, the assumption that each person is rational and will make decisions that are in their own best interest is often not accurate.
- Yes, but this is not an assumption of liberalism, but of economics in general.
Second, even if everyone was rational, the world is not always a fair place. There are often obstacles in the way of people achieving their goals, and not everyone has the same opportunities. This can lead to a situation where the most successful people are those who were born into privilege or who have other advantages, rather than those who are the most deserving.
- Yes, I fully agree. This is a problem in each and any political or economic system. Does the current western half socialist, half liberal systems improve the situation of underprivileged people - compared to a purely classical liberal system? We don't know.
Third, pure liberalism relies on a strong government to enforce the rules and to protect individual rights. In reality, governments are often corrupt or incompetent, and this can lead to a loss of liberty rather than an increase in it.
- Here I don't agree. Pure (really pure) liberalism refuses any government. It wants a "private law society" (as mentioned by the author), especially because governments are often corrupt or incompetent.