The simplest solution with the paradox of Fermi would be of saying that we didn’t observe anything due to the fact that there was nothing to observe. We are alone in the Galaxy or, at least, we are the first to have reached the threshold of technology.
This answer can sound reasonable first. It is possible that the probability of appearance of the intelligent life is so weak that the planet Earth is the only one in the Galaxy where it occurred. This assumption is nevertheless not very satisfactory because it seems to give again a special role to the Earth whereas throughout history, astronomy discoveries withdrew its central place in the universe.
Another solution consists in calling into question simulations of the civilization’s expansion in the Galaxy. Indeed, the space flights could be very fast but the colonization’s process could be much slower. The speed of colonization wouldn’t then be proportional to the speed of only one space flight. The duration for colonizing the Galaxy could be similar to the age of the Galaxy, which would explain why the solar system was not yet reached.
Certain solutions rest on the impossibility or the difficulty of space flights. It could be much more difficult or risky that what is gnerally assumed. Factors such as cosmic rays or interstellar dust could make it practically unrealizable. After all, a particle of a few tens of grams launched to a considerable fraction of the speed of light has a kinetic energy equivalent to a bomb of several kilotons.
Other explanations put forward psychological or sociological reasons. Thus a technological civilization could be very reticent to colonize other planets because the new colonies would end ineluctably up being turned over against their mother’s planet, a case which happened quite often in the history of humanity. Certain authors also suggested the possibility of a certain ethical code which would prohibit an advanced civilization to interference with another form of life. In this case, the history of humanity is not a good an example.