If you are an at-will employee, you can be fired for any reason or no reason, except unlawful discrimination. If you do not have an employment contract or union to represent you, your recourse is limited. Discrimination based on age, gender, race, religious beliefs etc.... may give rise to a different answer.
You might find my Legal Guide helpful "Workplace Discrimination: A Basis for Wrongful Termination Claims"
You might find my Legal Guide helpful "How to Choose a Lawyer for you.”
You might find my Legal Guide helpful "What Do I Tell My Lawyer"?
No one can know what the record is in the case because online we cannot find out any details. Check with a lawyer in your locale to discuss more of the details.
Good luck to you.
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My colleague is correct. Even if they were dead wrong as to the cause of the tardiness they still had the legal right to terminate you, especially during the probation period.
The response given is not intended to create, nor does it create an ongoing duty to respond to questions. The response does not form an attorney-client relationship, nor is it intended to be anything other than the educated opinion of the author. It should not be relied upon as legal advice. The response given is based upon the limited facts provided by the person asking the question. To the extent additional or different facts exist, the response might possibly change.
Wrongful termination means illegal discrimination (due to your age, gender, race, national origin, religion, etc.) or retaliation because of you being a "whistle blower," or doing something else protected by law, like union organizing.
It's not wrongful to terminate you if you were repeatedly tardy, or even if you weren't if you were an "at will" employee. Your employer can simply take a dislike to you, and fire you for no reason with no notice.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.