"No, I'm not bilingual; I'm not fluent in all my languages";
"I don't consider myself bilingual since I don't know how to write my other language";
"I didn't grow up with two languages, so I'm not bilingual";
"I have an accent in Spanish so I can't be considered bilingual" .....
I have heard such remarks repeatedly and I have always been dismayed that so many bilinguals depreciate their language skills.
The main reason is that the criterion of how fluent bilinguals are in their languages has long been dominant in how we characterize them. Even some linguists have put it forward as the defining characteristic. Hence, the American linguist, Leonard Bloomfield, stated that bilingualism is the native-like control of two languages.
The "real" bilingual has long been seen as the one who is equally, and fully, fluent in two languages. He or she is the "ideal", the "true", the "balanced", the "perfect" bilingual. All the others - in fact, the vast majority of bilinguals - are "not really" bilingual or are "special types" of bilinguals (see here for a longer discussion of this).
This two-monolinguals-in-one-person view has been assumed and amplified by many bilinguals themselves who either criticize their own language competence, or strive to reach monolingual norms, or even hide their knowledge of their weaker language(s).
If one were to count as bilingual only those people who pass as complete monolinguals in each of their languages (they are a rarity), one would be left with no label for the vast majority of people who use two or more languages regularly but who do not have native-like fluency in each. The reason they don't is quite simply that bilinguals do not need to be equally competent in all of their languages. They usually acquire and use their languages for different purposes, in different domains of life, with different people.
One of the fathers of bilingualism research, Uriel Weinreich, a linguist in the second part of the 20th century, recognized this and proposed, along with Canadian linguist William Mackey, a more realistic definition of bilingualism - the alternate use of two or more languages. My own definition is very similar: bilinguals are those who use two or more languages (or dialects) in their everyday lives.
This other way of looking at bilinguals allows one to include people ranging from the professional interpreter who is fluent in two languages all the way to the established immigrant who speaks the host country's language but who may not be able to read or write it. In between we find the bilingual child who interacts with her parents in one language and with her friends in another, the scientist who reads and writes articles in a second language (but who rarely speaks it), the member of a linguistic minority who uses the minority language at home only and the majority language in all other domains of life, the Deaf person who uses sign language with her friends but uses the written form of the spoken language with a hearing person, and so on. Despite the great diversity that exists between these people, they all lead their lives with more than one language.
The more recent and more realistic view of bilingualism has allowed many people who live with two or more languages to accept who they are - bilingual, quite simply. (See here for some feedback on what it is like to be bilingual).
Reference: "Describing bilinguals". Chapter 2 of Grosjean, François (2010). Bilingual: Life and Reality. Cambridge, Mass: Harvard University Press.
"Life as a bilingual" posts by content area: http://www.francoisgrosjean.ch/blog_en.html
François Grosjean's website: www.francoisgrosjean.ch