Why did some ancient people question whether Trajan adopted Hadrian?

The suspicion surrounding Hadrian’s adoption by Trajan stemmed primarily from the timing and circumstances of the announcement. Although Hadrian had been a long-time associate and was serving as governor of Syria at the time, Trajan had not previously indicated him as his chosen successor.12

When Trajan died in August 117, the news of his adoption of Hadrian was made public only after the emperor had already passed away. Because the announcement occurred at the very last minute, contemporary gossip suggested that the adoption was a fiction fabricated by the empress Plotina. Plotina was known to be on close terms with Hadrian and was a strong partisan of his, leading many to believe she had induced the dying emperor to name him as his successor. While historians generally consider it likely that the adoption was a genuine deathbed decision, the sequence of events—coupled with the fact that the army proclaimed Hadrian emperor immediately following the report of Trajan's death—has historically fueled speculation of a conspiracy.123