Let's look at the expression data of three genes in two groups. This is a subset of a real dataset comparing unpaired treated and untreated mouse colon organoids.
By looking at it, it seems like there's a clear difference in Cxcl2, there is likely no difference in Epcam, and there's clearly no difference in U2 (ok, there are two outliers).

df = data.frame(
  group=rep(c("a", "b", "c"), 6),
  U2=c(0, 0, 0, 0, 0, 452.939, 0, 0, 0, 215.705, 0, 427.984, 0, 0, 1411.686, 674.763, 0, 0),
  Cxcl2=c(6, 25, 6, 17, 20, 4, 2, 156, 6, 40, 1010.999, 35, 43, 98, 57, 16, 263, 54),
  Epcam=c(24818, 30270, 24818, 26090, 41797, 42059, 33214, 36154, 40872, 137463, 45677, 80316, 61955, 61683, 82049, 82288, 80172, 67598)
) |> dplyr::filter(group != "c")

If I use a generalized linear model with negative binomial famliy as a baseline, the statistics exactly reflect my gut feeling:

summary(glm(Cxcl2 ~ group, family = MASS::negative.binomial(2), data=df))$coefficients["groupb", "Pr(>|t|)"]
summary(glm(Epcam ~ group, family = MASS::negative.binomial(2), data=df))$coefficients["groupb", "Pr(>|t|)"]
summary(glm(U2 ~ group, family = MASS::negative.binomial(2), data=df))$coefficients["groupb", "Pr(>|t|)"]

[1] 0.004115246
[1] 0.5350445
[1] 0.9946097

However, when running DESeq2, suddenly U2 is by far the most significant gene (padj = 3.3e-17 !!):

dds = DESeqDataSetFromMatrix(
  df |> select(-group) |> t() |> round(),
  colData = df |> select(group),
  design = ~group
)
dds = DESeq(dds)
results(dds)

log2 fold change (MLE): group b vs a 
Wald test p-value: group b vs a 
DataFrame with 3 rows and 6 columns
        baseMean log2FoldChange     lfcSE      stat      pvalue        padj
       <numeric>      <numeric> <numeric> <numeric>   <numeric>   <numeric>
U2       77.4418      -25.71397  3.004014  -8.55987 1.12996e-17 3.38987e-17
Cxcl2    53.3127        1.73778  0.489112   3.55294 3.80956e-04 5.71434e-04
Epcam 62107.1289       -1.46626  0.453298  -3.23465 1.21790e-03 1.21790e-03

I don't understand that. Anything I'm doing wrong? If not, why does DESeq behave the way it does?

The average of U2 is different in a than it is in b. You can't expect DESeq to automatically remove outliers, if you judge that those two samples should be omitted, you should do that yourself. There are ways of filtering out genes where, say < 5 samples have more than 10 counts, that would have removed that gene from your dataset.