WIP BUG: Inconsistent date parsing of to_datetime

pandas/_libs/tslibs/parsing.pyx

@@ -3,6 +3,7 @@ Parsing functions for datetime and datetime-like strings.
 """
 import re
 import time
+import warnings
 
 from libc.string cimport strchr
 
@@ -149,14 +150,28 @@ cdef inline object _parse_delimited_date(str date_string, bint dayfirst):
         # date_string can't be converted to date, above format
         return None, None
 
+    swapped_day_and_month = False
     if 1 <= month <= MAX_DAYS_IN_MONTH and 1 <= day <= MAX_DAYS_IN_MONTH \
             and (month <= MAX_MONTH or day <= MAX_MONTH):
         if (month > MAX_MONTH or (day <= MAX_MONTH and dayfirst)) and can_swap:
             day, month = month, day
+            swapped_day_and_month = True
         if PY_VERSION_HEX >= 0x03060100:
             # In Python <= 3.6.0 there is no range checking for invalid dates
             # in C api, thus we call faster C version for 3.6.1 or newer
+
+            if dayfirst and not swapped_day_and_month:
+                warnings.warn(f"Parsing '{date_string}' in MM/DD/YYYY format.")
+            elif not dayfirst and swapped_day_and_month:
+                warnings.warn(f"Parsing '{date_string}' in DD/MM/YYYY format.")
+
             return datetime_new(year, month, day, 0, 0, 0, 0, None), reso
+
+        if dayfirst and not swapped_day_and_month:
+            warnings.warn(f"Parsing '{date_string}' in MM/DD/YYYY format.")
+        elif not dayfirst and swapped_day_and_month:
+            warnings.warn(f"Parsing '{date_string}' in DD/MM/YYYY format.")
+
         return datetime(year, month, day, 0, 0, 0, 0, None), reso
 
     raise DateParseError(f"Invalid date specified ({month}/{day})")

pandas/tests/tools/test_to_datetime.py

@@ -1752,6 +1752,60 @@ def test_dayfirst(self, cache):
         tm.assert_index_equal(expected, idx5)
         tm.assert_index_equal(expected, idx6)
 
+    def test_dayfirst_warnings(self):
+        # GH 12585
+
+        # CASE 1: valid input
+        arr = ["31/12/2014", "10/03/2011"]
+        expected = DatetimeIndex(
+            ["2014-12-31", "2011-03-10"], dtype="datetime64[ns]", freq=None
+        )
+
+        # A. dayfirst arg correct, no warning
+        res1 = to_datetime(arr, dayfirst=True)
+        tm.assert_index_equal(expected, res1)
+
+        # B. dayfirst arg incorrect, warning + incorrect output
+        res2 = to_datetime(arr, dayfirst=False)
+        with pytest.raises(AssertionError):
+            tm.assert_index_equal(expected, res2)
+
+        # C. dayfirst default arg, same as B
+        res3 = to_datetime(arr, dayfirst=False)
+        with pytest.raises(AssertionError):
+            tm.assert_index_equal(expected, res3)
+
+        # D. infer_datetime_format=True overrides dayfirst default
+        # no warning + correct result
+        res4 = to_datetime(arr, infer_datetime_format=True)
+        tm.assert_index_equal(expected, res4)
+
+        # CASE 2: invalid input
+        # cannot consistently process with single format
+        # warnings *always* raised
+
+        arr = ["31/12/2014", "03/30/2011"]
+        # first in DD/MM/YYYY, second in MM/DD/YYYY
+        expected = DatetimeIndex(
+            ["2014-12-31", "2011-03-30"], dtype="datetime64[ns]", freq=None
+        )
+
+        # A. use dayfirst=True
+        res5 = to_datetime(arr, dayfirst=True)
+        tm.assert_index_equal(expected, res5)
+
+        # B. use dayfirst=False
+        res6 = to_datetime(arr, dayfirst=False)
+        tm.assert_index_equal(expected, res6)
+
+        # C. use dayfirst default arg, same as B
+        res7 = to_datetime(arr, dayfirst=False)
+        tm.assert_index_equal(expected, res7)
+
+        # D. use infer_datetime_format=True
+        res8 = to_datetime(arr, infer_datetime_format=True)
+        tm.assert_index_equal(expected, res8)
+
     @pytest.mark.parametrize("klass", [DatetimeIndex, DatetimeArray])
     def test_to_datetime_dta_tz(self, klass):
         # GH#27733