The preposition a is often used to describe the means with which an action is realised. In English the most common prepositions used in this context are by and with. (There is no guarantee that all roman languages use the same pronouns as Portuguese.)
I go downtown by bycicle.
Spanish: Me voy al centro en bici.
Vou de bicicleta a cidade.
He wrote the text with a pencil.
Spanish: Escribio el texto con bolígrafo.
Escreveu o texto a caneta.
He drove off at high speed.
Spanish: Condujo con velocidad alta.
Dirigia em alta velocidade.
One can find that from a logical point of view with / com would be the best option, but logic is completely irrelevant in linguistics. However it seems that logic and use sometimes interfere and than we get several solutions.
There are webiste who are looking for a logic, Erros do costumez, and who even mean that an error is an error at a logical level. This approach leads nowhere. On the same website the user should choose the right option.
Qual a forma correcta?
a) comer com garfo e faca.
b) comer a garfo e faca.
c) comer de garfo e faca.
Following the author, a Portuguese native speaker, a) and b) are correct and that is true. However the reason given is not very convincing.
A resposta a esta questão pode encontrar-se recorrendo ao senso comum. Assim, eliminam-se, logo à partida, a hipótese b), pelo facto de a preposição a não nos fornecer a ideia de comer munido de... Assim restavam as hipóteses a) e c) que parecem ser ambas aceitáveis.
Comer com garfo e faca, transmite a ideia de utilização desses instrumentos para comer, tal como comer de faca e garfo. Portanto, e por não ter encontrado nada que contrariasse esta ideia, as hipóteses a) e c) podem considerar-se correctas.
The answer of this question can be deduced with common sense.Therefore we exclude from the very beginning option b), because the preposition a doesn't suggest the idea that we eat provided with a fork. Therefore only remains a) and c) that both seems acceptable.
In comer com garfo e faca we have the idea that instruments are used to eat and therefore and because there is no argument to refute that, we can consider the hypothesis a) and b) as correct.
It is well possible, that the common sense thinks that, because the common sense very often thinks and believes stupid things, but people with this common sense say "escrever a lápis" and lápis is an instrument. Actually the exact opposite is true and common sense uses very often the preposition a describe a means.
escrever a lápis
to write with a pencil.
escrever a caneta
to wirte with a ballpoint.
cortar a navalha
to cut with a flick-knife
cortar a faca
to cut with a knive
trancar a chave
to close the door by key
andar a pé
to go by foot
andar a cavalo
It is actually kind of obsession of hobby linguists, a phenomenon that can be observed all over the world, to explain linguistic structures with logic. A similar error is to explain the correct / incorrect use of words etymologically or by analogy. It is actually completely irrelevant where a word nowadays used steems from and whether it had a different meaning in ancient times. Only in the case that a word or a construction suggest something different than the actual meaning, there is a problem. If this is not the case, there is no problem. In other words, if the ancient meaning got completely lost, there is no problem.