Why can antibiotics treat flu-like symptoms caused by bacteria but are ineffective against flu?

Because the way antibiotics treat those symptoms is by killing the bacteria that cause them. If the symptoms are caused by viruses, then antibiotics can't help since they are not made to be able to "kill" viruses, just bacteria.

Flu viruses are not really living organisms like bacteria are. So viruses must be inactivated rather than killed. Antibiotics can neither kill nor inactivate viruses. They are created to be used to kill only specific bacteria, they do not kill every kind of bacteria, either. That is why there are so many different kinds of antibiotics.

Antibiotics can treat flu-like symptoms caused by some bacteria, because the right antibiotics can kill bacteria. So although flu like symptoms are similar to those of the flu, they are caused by different microbes so are not cured in the same way.