why does the system require that everyone is entitled to a fair trail, even if the person is caught red-handed

One word: Constitution

http://www.law.cornell.edu/constitution/

See Amendments IV, V, VI, and others.

The system requires that everyone is entitled to a fair trial because of the principle of justice, which is fundamental to the legal system. A fair trial ensures that individuals are treated impartially and that their rights are protected, regardless of their guilt or innocence.

Here's why the system ensures a fair trial, even for individuals caught red-handed:

1. Presumption of Innocence: In many legal systems, individuals are presumed innocent until proven guilty. Even if a person is caught red-handed, there might be factors at play that led to their actions, such as coercion or mental illness. By providing a fair trial, the legal system ensures that all evidence is presented and evaluated before concluding guilt.

2. Checks and Balances: A fair trial ensures that the justice system operates with checks and balances. It requires that the prosecution presents evidence to prove their case beyond a reasonable doubt. It also allows the defense to challenge the evidence, present counterarguments, and cross-examine witnesses. This process helps prevent wrongful convictions and ensures that justice is served.

3. Human Fallibility: The legal system recognizes that human beings are fallible and prone to errors. It is possible for the police or other authorities to make mistakes, mishandle evidence, or misinterpret the situation. A fair trial allows for these potential errors to be examined, corrected, or prevented, promoting a more accurate and just outcome.

4. Protecting Individual Rights: A fair trial is essential to protect the rights of individuals involved in criminal cases. It ensures that accused individuals have an opportunity to be heard, to present their defense, and to confront witnesses against them. This helps safeguard their constitutional rights, such as the right to due process, the right to a lawyer, and the right against self-incrimination.

In summary, the requirement for everyone to have a fair trial, even if they are caught red-handed, is a fundamental principle of justice. It promotes the principles of presumption of innocence, checks and balances, prevention of errors, and protection of individual rights.