Paper cannot be biased but an organization made up of people surely can. It is entirely possible for Twitter to be removing all kinds of pro-Erdogan messages or whatever, which might have made it biased. Erdogan's claim of bias is pure BS of course, but it is not something that is theoretically impossible.
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Police fire tear gas, detain 200, in Istanbul May Day scuffles (Reuters)
from the article: Turkey says Twitter is 'biased,' used for 'character assassinations'