The verb “argue” has two significantly different (but related) meanings. First, you can argue with someone about something (or over something), e.g.
The sentence means that Peter and his wife disagree, and they are actively trying to refute each other’s arguments. In other words, they argue against each other’s claims.
On the other hand, you can argue for something (i.e. express support to it) or argue that something must be true, as in
When you use the verb “argue”, one can always recognize the intended meaning from the preposition or conjunction used: “argue for/that” is always positive, “argue with/over/against/about” is always negative.
However, we do not have this luxury when using the adjectival form arguable. When something is “arguable”, it can be either argued for or argued against. For example,
The intended meaning remains elusive without further context. If I said the sentence above, it would mean that the claims of this article are defensible and that I believe they are true (since I am the author). However, if someone who doesn’t like me said the very same sentence, it would probably mean that the claims are debatable or dubious. When “arguable” is used in isolation, it is better to replace it with an unambiguous synonym, e.g. “tenable”, “credible”, or “defensible” in the positive case and “debatable”, “questionable”, “disputable” in the negative case.
When the adjective “arguable” is not used in isolation, it is possible to tell the intended meaning from the conjunction used. The conjunction “that” usually indicates the positive meaning, in accordance with the usage of “argue that”:
[One can argue that Kasparov is the best chess player of all time.]
The conjunction “whether” indicates disagreement:
[It is questionable whether it was a good idea.]
Finally, note that the adverbial form arguably always expresses the positive meaning. For example, the statement
[One can argue that Kasparov is the best chess player of all time.]
cannot be misconstrued as expressing that Kasparov’s status is questionable.