High-definition maps provide precise environmental information essential for prediction and planning in autonomous driving systems. Due to the high cost of labeling and maintenance, recent research has turned to online HD map construction using onboard sensor data, offering wider coverage and more timely updates for autonomous vehicles. However, the robustness of online map construction under adversarial conditions remains underexplored. In this paper, we present a systematic vulnerability analysis of online map construction models, which reveals that these models exhibit an inherent bias toward predicting symmetric road structures. In asymmetric scenes like forks or merges, this bias often causes the model to mistakenly predict a straight boundary that mirrors the opposite side. We demonstrate that this vulnerability persists in the real-world and can be reliably triggered by obstruction or targeted interference. Leveraging this vulnerability, we propose a novel two-stage attack framework capable of manipulating online constructed maps. First, our method identifies vulnerable asymmetric scenes along the victim AV's potential route. Then, we optimize the location and pattern of camera-blinding attacks and adversarial patch attacks. Evaluations on a public AD dataset demonstrate that our attacks can degrade mapping accuracy by up to 9.9%, render up to 44% of targeted routes unreachable, and increase unsafe planned trajectory rates, colliding with real-world road boundaries, by up to 27%. These attacks are also validated on a real-world testbed vehicle. We further analyze root causes of the symmetry bias, attributing them to training data imbalance, model architecture, and map element representation. To the best of our knowledge, this study presents the first vulnerability assessment of online map construction models and introduces the first digital and physical attack against them.