What is meant by the black thread in the verse is the night, and the white thread is the dawn, not the rising of the sun.
Dawn is called the white thread because the first thing that is seen of the dawn is a light in the sky that looks like a thread along the horizon, stretching from right to left, from north to south. Then it continues to increase until it spreads through the whole sky. See Fath al-Baari, commentary on hadeeth no. 1917.
Al-Bukhaari (1916) and Muslim (1090) narrated that ‘Adiyy ibn Haatim (may Allaah be pleased with him) said: “When the words ‘until the white thread (light) of dawn appears to you distinct from the black thread (darkness of night)’ [al-Baqarah 2:187 – interpretation of the meaning] were revealed, I took a black rope and a white rope and put them beneath my pillow, and I started to look at them during the night, but I could not see any distinction between them. The next morning I went to the Messenger of Allaah (peace and blessings of Allaah be upon him) and told him about that. He said, ‘Rather that is the blackness of the night and the whiteness of the day.’”
Al-Nawawi (may Allaah be pleased with him) said:
Abu ‘Ubayd said: The white thread is the true dawn and the black thread is the night.
And Allaah knows best.