The structure 可毕竟
"..., but still..."
The structure …可毕竟… 
is used to express opposition.
Using this construction, the first part of the sentence states a fact. In the second part of the sentence, a justification or refutation is stated after 可毕竟.
is used to express opposition.
Using this construction, the first part of the sentence states a fact. In the second part of the sentence, a justification or refutation is stated after 可毕竟.Scheme
fact
可毕竟
justification/refutation
Examples
虽然他不是故意的，可毕竟做错了事，因该受到批评
Although he didn’t do it on purpose, he still did something wrong and deserves criticism
suīrán tā bú shì gùyì de, kě bìjìng zuòcuò le shì, yīngāi shòudào pīpíng
我原以为这次考试不及格了，可毕竟还是及格了
I thought I would fail this exam, but I actually passed it
wǒ yuán yǐwéi zhè cì kǎoshì bù jígé le, kě bìjìng háishì jígé le
房子小是小，可毕竟是我们自己的家，我已经很满足了
Of course, the apartment is small, but at least it is ours. I am happy about it
fángzi xiǎo shì xiǎo, kě bìjìng shì wǒmen zìjǐ de jiā, wǒ yǐjīng hěn mǎnzú le
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