The Twitter app makes use of an in-app web browser to open external links shared in tweets. Links are automatically displayed in their WebView, which unfortunately lacks the basic features of a regular web browser.
If you would like Twitter to open links with your mobile web browser, here are the instructions on how to turn off the app's WebView.
How To Disable Twitter In-App Web Browser
Open the Twitter app and tap on the Ellipsis menu. Go to Settings > General > Use in-app browser and clear the Open external links with Twitter browser checkbox: